# NCERT Mathematics Class 10 Exemplar Ch 5 Arithmetic Progressions Part 7 (For CBSE, ICSE, IAS, NET, NRA 2023)

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EXERCISE 5.4

1. The sum of the first five terms of an AP and the sum of the first seven terms of the same AP is 167. If the sum of the first ten terms of this AP is 235, find the sum of its first twenty terms.

2. Find the

(i) Sum of those integers between 1 and 500 which are multiples of 2 as well as of 5.

(ii) Sum of those integers from 1 to 500 which are multiples of 2 as well as of 5 . (iii) sum of those integers from 1 to 500 which are multiples of 2 or 5. [Hint

(iii) These numbers will be: multiples of multiples of multiples of 2 as well as of 5

(ii) 12750

(iii) 75250

3. The eighth term of an AP is half its second term and the eleventh term exceed one third of its fourth term by 1. Find the 15th term.

4. An AP consists of 37 terms. The sum of the three middle most terms is 225 and the sum of the last three is 429. Find the AP.

5. Find the sum of the integers between 100 and 200 that are

(i) divisible by 9 (ii) not divisible by 9

[Hint (ii) : These numbers will be: Total numbers – Total numbers divisible by 9]

6. The ratio of the 11th term to the 18th term of an AP is 2: 3. Find the ratio of the 5th term to the 21st term, and also the ratio of the sum of the first five terms to the sum of the first 21 terms.

7. Show that the sum of an AP whose first term is a, the second term b and the last term c, is equal to

8. Solve the equation .