- Introduction
- |
- What is arithmetic progression
- |
- Some Important points about AP
- |
- nth term of Arithmetic Progression
- |
- Sum of nth item in Arithmetic Progression

Given below are the

a) Concepts questions

b) Calculation problems

c) Multiple choice questions

d) Long answer questions

e) Fill in the blank's

- Find the sum of m terms of an A. P. whose n
^{th}terms is given by a_{n}= 5 – 6n. - Find the sum of all even integers between 101 and 999.
- In an A. P., if the 5
^{th}and 12^{th}terms are 30and 65 respectively, what is the sum of first 20 term? - If the sum of 7 terms of an A. P. is 49 and that of 17 terms is 289, find the sum of n terms.
- In an A. P., the sum of first n terms is . Find its 25
^{th}term. - A man arranges to pay off a debt of Rs 3600 by 40 annual installments which form an arithmetic series. When 30 of the instalments are paid, he dies leaving one – third of the debt unpaid, find the value of the first installment.
- There are 25 trees at equal distances of 5m in a line with a well, the distance of the well from the nearest tree being 10m. A gardener waters all the trees separately starting from the well and he returns to the well after watering each tree to get water for the next. Find the total distance the gardener will cover in order to water all the trees.
- A man is employed to count Rs 10710. He counts at the rate of Rs 180 per minute for half an hour. After this he counts at the rate of Rs 3 less every minute than the preceding minute. Find the time taken by him to count the entire amount.
- A sum of Rs 700 is to be used to give seven cash prizes to students of a school for their overall academic performances. If each price is R 20 less than its preceding prize, fid the value of each prize.
- In an A. P. the first term is 8, n
^{th}term is 33 and the sum to first n terms is 123. Find n and d, the common differences. - The first and the last term of an A. P. are 17 and 350 respectively. If the common difference is 9, how many terms are there and what is their sum?
- In an A. P., the first term is 2, the last term is 29 and the sum of the terms is 155. Find the common difference of the A. P.
- In an A. P., the sum of first ten terms is -150 and the sum of its next ten terms are -550. Find the A. P.

1. m (2 - 3m)

2. 246950

3. 1150

4. n

5. 80

6. Rs 51

7. 3500m

8. 89 minutes

9. Rs 105000

10. n = 6, d = 5

11. n = 38, S = 6973, a

12. 3

13. a = 6, d = -4

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