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If the sum of first 7 terms of an AP is 49 and that of 17 term

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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.

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Text solutionVerified

Solution: given that

s_{7} = 49 = 7^{2} (s_{n} = n^{2})

s_{17} = 289 = 17^{2}

now

s_{n} = \frac{n}{2} [2 a + (n - 1) d]

s_{7} = \frac{7}{2} [2 a + (7 - 1) d]

49 = \frac{7}{2} [2 a + 6 d]

7 = a + 3 d

eqn(1)
now

S_{17} = \frac{17}{2} [2 a + (17 - 1) d]

289 = \frac{17}{2} [2 a + 16 d]

a + 8 d = 17

eqn(2)
subtracting eqns (1) & (2)
we get

5 d = 10

d = 2

puting it in eqn (1)

a + 3 (2) = 7

a = 1

s_{n} = \frac{n}{2} [2 a + (n - 1) d]

s_{n} = \frac{n}{2} [2 + (n - 1) 2]

= \frac{n}{2} [2 + 2 n - 2]

s_{n} = n^{2}

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Question Text	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 Type	Text solution:1
Upvotes	150