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

In this Question the sum of first two terms of an AP is given. you have to find the sum of n term of this AP.

This is the Question Number 27 Of Exercise 11 C of RS Aggarwal Solution

Deepak BoraNewbie

# If the sum of first 7 terms of an AP is 49 and that of first 17 terms is 289, find the sum of first n terms.

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Given that,

S_7 = 49

S_17 = 289

S_7

= 7/2 [2a + (n – 1)d]

S_7 = 7/2 [2a + (7 – 1)d]

49 = 7/2 [2a + 16d]

7 = (a + 3d)

a + 3d = 7 … (i)

Similarly,

S_17 = 17/2 [2a + (17 – 1)d]

289 = 17/2 (2a + 16d)

17 = (a + 8d)

a + 8d = 17 … (ii)

Subtracting equation (i) from equation (ii),

5d = 10

d = 2

From equation (i),

a + 3(2) = 7

a + 6 = 7

a = 1

S_n = n/2 [2a + (n – 1)d]

= n/2 [2(1) + (n – 1) Ã— 2]

= n/2 (2 + 2n – 2)

= n/2 (2n)

= n2