Question

if the sum of the first 7 terms of an ap is 119 and that of the first 17 terms is 714 and find the sum of its first n terms​

Answer 1

Answer:

Required sum is  n/2 × [4+(n-1)5]

Step-by-step explanation:

Let a be the first term

and d be the common difference

sum of first 7 terms is

S(7) = 7/2 [2a+(7-1)d] = 119

⇒  [2a+6d] = 34

⇒ a + 3d = 17 → (1)

sum of first 17 terms is

S(17) = 17/2 [2a+(17-1)d] = 714

⇒ a + 8d = 42 → (2)

(2) - (1) ⇒

5d = 25

⇒ d = 5

∴ a = 2

the sum of its first n terms​ is

S(n) = n/2 × [4+(n-1)5]

Answer 2

Answer:

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