Please refer to Arithmetic Progression MCQ Questions Class 10 Mathematics below. These MCQ questions for Class 10 Mathematics with answers have been designed as per the latest NCERT, CBSE books, and syllabus issued for the current academic year. These objective questions for Arithmetic Progression will help you to prepare for the exams and get more marks.

**Arithmetic Progression MCQ Questions Class 10 Mathematics**

Please see solved MCQ Questions for Arithmetic Progression in Class 10 Mathematics. All questions and answers have been prepared by expert faculty of standard 10 based on the latest examination guidelines.

**MCQ Questions Class 10 Mathematics Arithmetic Progression**

**Question. If a, b, c, d, e, f are A.M.s between 2 and 12, then a + b + c + d + e + f is equal to :- **

(a) 14

(b) 84

(c) 42

(d) None

**Answer**

C

**Question. For the A.P. a + (a + d) + (a + 2d) + …. + l of n terms :- **

(a) S_{n} = n/ 2 (a + l)

(b) S_{n} = n/ 2 {2a + (n−1) d}

(c) S_{n} = n /2 {2*l* − (n−1) d}

(d) S_{n} = ( l−a +d)(a+*l*)/ad

(e) All of these

**Answer**

E

**Question. If the nth term of an A.P. is 4n + 1, then the common difference is **

(a) 3

(b) 4

(c) 5

(d) 6

**Answer**

B

**Question. 30 trees are planted in a straight line at intervals of 5 m. To water them, the gardener needs to bring water for each tree, separately from a well, which is 10 m from the first tree in line with the trees. How far will he have to walk in order to water all the trees beginnings with the first tree ? Assume that he starts from the well. **

(a) 4785 m

(b) 4795 m

(c) 4800 m

(d) None of these

**Answer**

B

**Question. If a, b, c are in A.P. then :-**

(a) the equation (b − c) x^{2} + (c − a) x + (a − b) = 0, b ≠ c has equal roots

(b) a^{2}, b^{2}, c^{2} are in A.P.

(c) λa + µ, λb + µ, lc + µ are in A.P., λ, µ ∈ R

(d) None of these

**Answer**

A,C

**Question. Let a _{1}, a_{2},…….a19 be the first 19 terms of an arithmetic progression where a_{1}+a_{8}+a_{12}+a_{19}=224. The sum a_{1} + a_{2}+ a_{3} +…+a_{19} is equal to **

(a) 896

(b) 969

(c) 1064

(d) 1120

**Answer**

C

**Question. Given that n A.M.’s are inserted between two sets of numbers a, 2b and 2a, b, where a, b Î R. If the mth means in the two cases are same then ratio a : b is equal to :- **

(a) n : (n − m + 1)

(b) (n − m + 1) : m

(c) (n − m + 1) : n

(d) m : (n − m + 1)

**Answer**

D

**Question. How many terms are there is an AP whose first and fifth terms are 14 and 2 respectively and the sum of terms is 40? **

(a) 15

(b) 10

(c) 5

(d) 20

**Answer**

B

**Question. The next term of the sequence 9, 16, 27, 42, ……… is :- **

(a) 53

(b) 61

(c) 57

(d) None

**Answer**

B

**Question. The infinite sum 1+4/7+9/7 ^{2}+16/7^{3}+25/7^{4} +……… equals **

(a) 27/ 14

(b) 21/ 13

(c) 49 /27

(d) 256 /147

**Answer**

C

**Question. The sums of first n terms of two A.P.’s are in the ratio (3n + 8) : (7n + 15). The ratio of their 12th terms is :- **

(a) 4/ 9

(b) 7 /16

(c) 3 /7

(d) None

**Answer**

B

**Question. The sum of 3rd and 15th elements of an arithmetic pr gression is equal to the sum of 6th, 11th and 13th elements of the same progression. Then which element of the series should ecessarily be equal to zero ? **

(a) 1st

(b) 9th

(c) 12th

(d) None of these

**Answer**

C

**Question. A person pays Rs. 975 in monthly instalments, each monthly instalment being less than the former by Rs. 5. The amount of the first instalment is Rs. 100. In what tune, will the entire amount be paid ? **

(a) 12 months

(b) 26 months

(c) 15 months

(d) 18 months

**Answer**

C

**Question. The sum of first n terms of an A.P. whose last term is l and common difference is d is :- **

(a) n/ 2 [2l + (n − 1) d]

(b) n/ 2 [2

*l*− (n − 1) d]

(c) n/ 2 [

*l*+ (n − 1) d]

(d) n /2 [

*l*− (n − 1) d]

**Answer**

B

**Question. If the sides of a right triangle are in A.P., then the ratio of its smallest side to the greatest side is :- **

(a) 3 : 4

(b) 3 : 5

(c) 4 : 5

(d) None

**Answer**

C

**Question. In an A.P., sum of first n terms is 2n ^{2} + 3n, it’s common difference is :- **

(a) 4

(b) 3

(c) 2

(d) 6

**Answer**

A

**Question. The sum of all numbers from 1 to 1000 which are neither divisible by 2 nor by 5 is :- **

(a) 200000

(b) 500500

(c) 250000

(d) None of these

**Answer**

A

**Question. The number of terms common to the arithmetic progressions 3, 7, 11, ……., 407 and 2, 9, 16,….., 709 is :- **

(a) 51

(b) 14

(c) 21

(d) 28

**Answer**

B

**Question. How many multiples of 7 are there between 33 and 329 ? **

(a) 43

(b) 35

(c) 329

(d) 77

**Answer**

A

**Question. If a ^{n} + b^{n}/a^{n−1} +b^{n−1} be the arithmetic mean between a and b, then the value of n is :- **

(a) 1

(b) 0

(c) − 1/ 2

(d) −1

**Answer**

A

**Question. The n ^{th} term of the sequence 2, 5, 11, 20, 32, …………. is :- **

(a) 3n

^{2}+3n−4/2

(b) 3n

^{2}+3n+4/2

(c) 3n

^{2}+3n+4/2

(d) None of these

**Answer**

B

**Question. A club consists of members whose ages are in AP, the common difference being 3 months. If the youngest member of the club is just 7 years old andhe sum of the ages of all the members is 250 year, then the number of members in the club are **

(a) 15

(b) 20

(c) 25

(d) 30

**Answer**

C

**Question. The sum of 12 terms of an A.P. whose first term is 4, is 256. What is the last terms ? **

(a) 35

(b) 36

(c) 37

(d) 116/3

**Answer**

C

**Question. If the sum of first n terms of an A.P. is Pn + Qn ^{2} where P and Q are constants, then common difference of A.P. will be :- **

(a) P + Q

(b) P − Q

(c) 2P

(d) 2Q

**Answer**

D

**Question. The sum of n terms of a series is An ^{2} + Bn, then the nth term is :- **

(a) A(2n − 1) − B

(b) A(1 − 2n) + B

(c) A(1 − 2n) − B

(d) A(2n − 1) + B

**Answer**

D

**Question. Sum of first n terms of an A.P. is an(n − 1). The sum of squares of these terms is :- **

(a) a^{2}/ 6 n(n − 1) (2n − 1)

(b) 2a^{2}/ 3 n(n + 1) (2n + 1)

(c) a^{2}n^{2}(n − 1)^{2}

(d) 2a^{2} /3 n(n − 1) (2n − 1)

**Answer**

D

**Question. If x, y, z are in A.P., then (x + 2y − z) (x + z − y) (z + 2y − x) is equal to :- **

(a) xyz

(b) 2xyz

(c) 4xyz

(d) None

**Answer**

C

**Question. The value of n, for which a ^{n+1} +b^{n+1}/a^{n} +b^{n} is the A.M. between a and b is :- **

(a) 0

(b) 1

(c) − 1/ 2

(d) −1

**Answer**

A

**Question. The nth term of the series 1+1/1+3 + 1/1+3+5 + ……. is :- **

(a) 2/ n(n1) +

(b) 1/ n^{2}

(c) n^{2}

(d) None

**Answer**

B

**Question. For an A.P., kn n S S is independent of n. The value of d a for this A.P. is :- **

(a) 1

(b) 2

(c) 3

(d) 4

**Answer**

C

**Question. If the angles A < B < C of a triangle are in A.P. then :- **

(a) c^{2} = a^{2} + b^{2} − ab

(b) b^{2} = a2 + c^{2} − ac

(c) c^{2} = a^{2} + b^{2}

(d) None of these

**Answer**

C

**Question. A man arranged to pay off a debt of Rs.3600 in 40 annual instalments which form an Arithmetical Progression. When 30 of the instalments are paid, he dies leaving one third of the debt unpaid. Find the value of the 1 instalment is **

(a) Rs.55

(b) Rs.53

(c) Rs.51

(d) Rs.49

**Answer**

C

**Question. Let S _{n} denote the sum of the first ‘n’ terms of an A.P. S_{2n}= 3S_{n}. Then, the ratio S_{3n}/S_{n} is equal to **

(a) 4

(b) 6

(c) 8

(d) 10

**Answer**

B

**Question. In an A.P. sum of first p terms is equal to the sum of first q terms. Sum of it’s first p + q terms is :- **

(a) − (p + q)

(b) p + q

(c) 0

(d) None

**Answer**

C

**Question. 2,√6 , 4.5 are the following terms of an A.P.. **

(a) 101st, 207th, 309th

(b) 101st, 201st, 301st

(c) 2nd, 6th, 9th

(d) None of these

**Answer**

D

**Question. If 3+5+7+………+nterms/ 5+8+11+……+10 terms = 7, then the value of n is **

(a) 35

(b) 36

(c) 37

(d) 40

**Answer**

A

**Question. If an A.P., S _{m} : S_{n} :: m^{2} : n^{2}. The ratio of the pth term to qth term is :- **

(a) p−1/q−1

(b) p/ q

(c) 2p −1/ 2q −1

(d) None

**Answer**

C

**Question. If the sum of first n natural numbers is one-fifth of the sum of their squares, then n is **

(a) 5

(b) 6

(c) 7

(d) 8

**Answer**

C

**Question. The sum of 40 A.M’s between two numbers is 120. The sum of 50 A.M’s between them is equal to :- **

(a) 130

(b) 160

(c) 150

(d) None

**Answer**

C

**Question. If x, y, z are in A.P., then (x + y − z) (y + z − x) is equal to :- **

(a) 8xy + 3y^{2} − 4x^{2}

(b) 8xy − 3y^{2} − 4x^{2}

(c) 8xy − 3x^{2} + 4y^{2}

(d) 8xy − 3y^{2} + 4x^{2}

**Answer**

B

**Question. I open a book store with a number of books. On the first day, I sell 1 book; on the second day, I sell 2 books; on the third day, I sell 3 books and so on. At the end of the month (30 days). I realise that I sold the same number of books with which I started. Find the number of books in the beginning. **

(a) 365

(b) 420

(c) 465

(d) 501

**Answer**

C

**Question. If S denotes the sum of first n terms of the A.P. a + (a + d) + (a + 2d) + ……. whose nth term is l, then the common ‘d’ of the A.P. is :- **

(a) l −a/n

(b) *l*^{2}−a^{2}/2S−a+*l*

(c) *l*^{2}−a^{2}/2S−a+*l*

(d) None of these

**Answer**

A

**Question. For the A.P. x + (x + 1) + (x + 2) + …… + y **

(a) C. D. is 1

(b) Numer of terms is y − x + 1

(c) Sum of the series is y−x+1/2(x+y)

(d) All of these

**Answer**

D

**Question. There are two arithmetic progressions, A1 and A2, whose first terms are 3 and 5 respectively and whose common differences are 6 and 8 respectively. How many terms of the series are common in the first n terms of A _{1} and A_{2}, if the sum of the nth terms of A1 and A2 is equal to 6,000? **

(a) 103

(b) 107

(c) 109

(d) 113

**Answer**

B

**Question. Find the sum of all natural numbers not exceeding 1000, which are divisible by 4 but not by 8. **

(a) 62500

(b) 62800

(c) 64000

(d) 65600

**Answer**

A

**Question. The second term of the sequence defined by a _{n} = 3n + 2 is **

(a) 2

(b) 4

(c) 6

(d) 8

**Answer**

D

**Question. If a _{n} = 5n – 4 is a sequence, then a_{12} is **

(a) 48

(b) 52

(c) 56

(d) 62

**Answer**

C

**Question. If a _{n} = 3n – 2, then the value of a_{7} + a_{8} is **

(a) 39

(b) 41

(c) 47

(d) 53

**Answer**

B

**Question. The first term of an AP is p and the common difference is q, then its 10th term is **

(a) q + 9p

(b) p – 9q

(c) p + 9q

(d) 2p + 9p

**Answer**

C

**Question. If 4/5 , a, 2 are three consecutive terms of an AP, then the value of a is **

(a) 5/2

(b) 2/7

(c) 5/7

(d) 7/5

**Answer**

A

**Question. In an AP, if d = – 4, n = 7, an = 4, then a is **

(a) 6

(b) 7

(c) 20

(d) 28

**Answer**

D

**Question. The n ^{th} term of the AP: a, 3a, 5a, … is **

(a) na

(b) (2n – 1)a

(c) (2n + 1)a

(d) 2na

**Answer**

B

**Question. If the sum to n terms of an AP is 3n ^{2} + 4n, then the common difference of the AP is **

(a) 7

(b) 5

(c) 8

(d) 6

**Answer**

D

**Question. The sum of all natural numbers which are less than 100 and divisible by 6 is **

(a) 412

(b) 510

(c) 672

(d) 816

**Answer**

D

**Question. If a, b, c are in AP then ab + bc = **

(a) b

(b) b^{2}

(c) 2b^{2}

(d) 1/b

**Answer**

C

**Question. The sum of first five terms of the AP: 3, 7, 11, 15, … is: **

(a) 44

(b) 55

(c) 22

(d) 11

**Answer**

B

**Question. If the first term of an AP is 1 and the common difference is 2, then the sum of first 26 terms is **

(a) 484

(b) 576

(c) 676

(d) 625

**Answer**

C

**Question. In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:****(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).****(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).****(c) Assertion (A) is true but reason (R) is false.****(d) Assertion (A) is false but reason (R) is true.**

**Question. Assertion (A): Common difference of the AP: –5, –1, 3, 7, … is 4. ****Reason (R): Common difference of the AP : a, a + d, a + 2d, … is given by d = 2 ^{nd} term – 1^{st} term.**

**Answer**

A

**Question. Assertion (A): If nth term of an AP is 7 – 4n, then its common difference is – 4. ****Reason (R): Common difference of an AP is given by d = a ^{n+1} – an.**

**Answer**

A

**Question. Assertion (A): Common difference of an AP in which a _{21} – a_{7} = 84 is 14. **

**Reason (R): nth term of an AP is given by a**

_{n}= a + (n – 1) d.**Answer**

D

**In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:****(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).****(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).****(c) Assertion (A) is true but reason (R) is false.****(d) Assertion (A) is false but reason (R) is true.**

**Question. Assertion (A): The arrangement of numbers, i.e., – 4, 16, – 64, 256, – 1024, 4096, … form a sequence. ****Reason (R): An arrangement of numbers which are arranged in a definite order according to some rule, is called a sequence.**

**Answer**

A

**Question. Assertion (A): Sequence 1, 5, 9, 13, 17, 21, … is a finite sequence. ****Reason (R): A sequence with finite number of terms or numbers is called a finite sequence**

**Answer**

D

**(a) If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.****(b) If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.****(c) If Assertion is correct but Reason is incorrect.****(d) If Assertion is incorrect but Reason is correct.**

**Question. Assertion : The sum of the series with the nth term, t _{n} = (9 – 5n) is (465), when no. of terms n = 15. **

**Reason : Given series is in A.P. and sum of n terms of an A.P. is S**

_{n}= n/2[2a + (n −1) d] .**Answer**

D

**Question. Assertion : Sum of first 10 terms of the arithmetic progression – 0.5, – 1.0, – 1.5, ………………………. is 27.5. ****Reason : Sum of n terms of an A.P. is given as S _{n} = n/2[2a + (n −1) d] where a = first term, d = common difference.**

**Answer**

A

**Question. Assertion : If n ^{th} term of an A.P. is 7 – 4n, then its common difference is –4. **

**Reason : Common difference of an A.P. is given by d = a**

_{n}+ 1 – a_{n}.**Answer**

A

**Question. Assertion : If S _{n} is the sum of the first n terms of an A.P., then its nth term an is given by an = S_{n} – S_{n} – 1 . Reason : The 10^{th} term of the A.P. 5, 8, 11, 14, ………………. is 35.**

**Answer**

C

**Question. Assertion : Let the positive numbers a, b, c be in A.P., then 1/bc , 1/ac , 1/ab are also in A.P. ****Reason : If each term of an A.P. is divided by abc, then the resulting sequence is also in A.P.**

**Answer**

A

**Question. Assertion : Arithmetic between 8 and 12 is 10. ****Reason : Arithmetic between two numbers ‘a’ and ‘b’ is given as . a + b/2**

**Answer**

A

**Question. Assertion : Sum of first hundred even natural numbers divisible by 5 is 500. ****Reason : Sum of first n-terms of an A.P. is given by S _{n} = n/2[2a + (n −l) d] where l = last term.**

**Answer**

D