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
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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) × 2]
= n/2 (2 + 2n – 2)
= n/2 (2n)
= n2