# 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.

Answer: 970

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

Answer: (i) 12250

(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 15^{th} term.

Answer: 3

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.

Answer:

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]

Answer: (i) (ii)

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

Answer: ;

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 .

Answer: 50

9. Jaspal Singh repays his total loan of ₹ 118000 by paying every month starting with the first instalment of ₹ 1000. If he increases the instalment by ₹ 100 every month, what amount will be paid by him in the 30^{th} instalment? What amount of loan does he still have to pay after the 30^{th} instalment?

Answer: ₹ 3900; ₹ 44500

10. The students of a school decided to beautify the school on the Annual Day by fixing colourful flags on the straight passage of the school. They have 27 flags to be fixed at intervals of every 2 m. The flags are stored at the position of the middle most flag. Ruchi was given the responsibility of placing the flags. Ruchi kept her books where the flags were stored. She could carry only one flag at a time. How much distance did she cover in completing this job and returning back to collect her books? What is the maximum distance she travelled carrying a flag?

Answer: