Please refer to Arithmetic Progression HOTs Class 10 Mathematics provided below with Arithmetic Progression. All HOTs for Class 10 Mathematics with answers provided below have been designed as per the latest syllabus and examination petter issued by CBSE, NCERT, KVS. Students of Standard 10 Mathematics should learn the solved HOTS for Class 10 Mathematics provided below to gain better marks in examinations.

**Arithmetic Progression Class 10 Mathematics HOTs**

**Questions of 1 Mark**

**Question.** Find the 10th term from the end of A.P**3, 8, 13, 18…253**

## Answer

209

**Question.****Which term of the sequence 4,9,14…is 124?**

## Answer

n = 25

**Question.** How many numbers of two digits are divisible by 8?

## Answer

n = 11

**Question.** For what value of K, the number x, 2x + k, 3x + 6,are three consecutive terms of A.P

## Answer

k=3

**Question.** Write next term of A.P ∫8, ∫18, ∫32….

## Answer

5√2, 6√2, 7√2

**Question.** Find the middle term of A.P**1,8,15,…,505**

## Answer

middle term = 73

**Question.****Find first three terms of an A.P whose nth term is -5 + 2x**

## Answer

**–3, -1, 1**

**Question.** What is the common difference of an A.P in which a_{23} – a_{18} = 45

## Answer

**d = 9**

**Question.****Find the sum of all odd integers between 1 and 100 which are not multiples of 4**

## Answer

2500

**Question.** In the given A.P, find the missing terms 0,_,-8,-12,_.

## Answer

**0,-4,-8,-12,-16**

**Questions of 2 Mark**

**Question.** If the 10th term of an A.P is 47 and first term is 2, find the sum of the first 15 terms

## Answer

255

**Question.****How many terms of A.P 18, 16, 14…Should be taken so that their sum is zero?**

## Answer

19

**Question.****Which term of A.P 121,117,113….is the first negative term?**

## Answer

32^{nd} term

**Question.** Solve the equation – 2 + 5 + 8… + x = 155

## Answer

29

**Question.** If the sum of n terms of an A.P is n^{2} + 2x, find the A.P and the 20^{th} term.

## Answer

3,5,7,9

T20 = 41

**Question.** How many multiples of 4 lie between 10 and 250?

## Answer

60

**Question.** Determine the A.P whose zero term is 16 and when 5^{th} term is subtracted from 7^{th} ,we get 12

## Answer

4,10,16,22

**Question.** If seven times the seventh term of an A.P is equal to 11 times the eleventh term, show that 18^{th} term of an A.P is zero.

## Answer

a + 17d = 0

T_{18} = 0

**Question.** For what values of n, nth term of the series 3, 10, 17…and 63,65,67…are equal?

## Answer

n = 13