Question

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

Answer 1

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Given:- S7= 49, S17=289

Sum of n terms given by formula

$sn = \frac{n}{2} {2a + (n - 1)d}$

where, S = Sum,

n = number of terms,

a = first term and d = common difference.

S7 = 49

Therefore,

49=7/2{2a+(7-1)d}

⇒ 49 = 7(a + 3 d)

⇒ 7= a + 3 d

⇒ a + 3 d = 7 [1]

Similarly,

S17=17/2[a+(17-1)d]

289 = 17(a + 8 d)

17 = a + 8 d

a + 8 d = 17 [2]

Subtracting [1] from [2] we get;

a + 8 d – a – 3 d = 17 – 7

⇒ 5 d = 10

⇒ d = 2

Using value of d in eqn. (1)

a+3d=7

a+6=7

a=1

then, by using value of a and d.

$sn = \frac{n}{2} {2(1) + (n - 1)2} \\ sn = \frac{n}{2} {2 + 2n - 2} \\ s = {n}^{2}$

Hope it helps you ❣️☑️