# NCERT Class 10 Mathematics Arithmetic Progression Worksheet 3 CBSE Board Sample Problems (For CBSE, ICSE, IAS, NET, NRA 2023)

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## Arithmetic Progression Worksheet 3

Question 1

The sum of four consecutive numbers in an AP is 32 and the ratio of the product of the first and the last terms to the product of the two middle terms is 7: 15. Find the numbers.

Answer: (2, 6,10, 14)

Question 2

Find the sum of 3 digit numbers which are not divisible by 7?

Answer: 424214

Question 3

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

Answer:

Question 4

Find the sum of all three-digit numbers, which leave the remainder 3 when divided by 5

Answer: 99090

Question 5

In an AP, if and , find the value of k.

Answer: 27

Question 6

If Sn denotes the sum of first n terms of an AP, prove that

Answer:

Question 7

If the pth, qth & rth term of an AP is x, y and z respectively, show that

Answer:

Question 8

Find the 20^{th} term from the end of the AP 3,8, 13 … 253

Answer:

Question 9

The sum of the first n terms of an AP whose first term is 8 and the common difference is 20 is equal to the sum of first 2n terms of another AP whose first term is — 30 and the common difference is 8. Find n.

Answer:

Question 10

Determine k so that are three consecutive terms of an AP

Answer: k = 0