In this Question the sum of first two n terms of the AP is given. You have to find the first term and common difference of the AP.

This is the Important question based on Arithmetic progression Chapter of R.S Aggarwal book for ICSE & CBSE Board.

This is the Question Number 28 Of Exercise 11 C of RS Aggarwal Solution

# The sum of the first 9 terms of an AP is 81 and the sum of its first 20 term is 400. Find the first term and the common difference of the AP.

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Let

First term be p , Common difference be d

Now,

First Situation,

2p + 8d =18 ……. (1)

Second Situation,

2p + 19d = 40 …… (2)

Now,

Subtract (1) from (2),

(2p + 19d) – (2p + 8d) = 40 – 18

11d = 22

d = 2

Substitute the value of d in (1),

2p + 16 = 18

2p = 18 – 16

2p = 2

p = 2/2

p = 1

Therefore,

First term = 1 and common difference = 2