Question

FIND THE FIRST N TERMS​

Answer 1

$Question:$

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.

$Solution:$

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

⇒ 49 = $\frac{7}{2}$[2a + (7-1)d]

⇒ 14 = 2a + 6d

∴ a + 3d = 7.........(i)

Again,

⇒ 289 = $\frac{17}{2}$[2a+(17-1)d]

⇒ 34 = 2a + 16d

∴ a + 8d = 17.............(ii)

By solving for a and d , we get

a = 1

d = 2

• Sum of first n terms of AP = $\frac{n}{2} [2 +(n-1)2]$

                                                     = $\frac{n}{2}$×2 n

                                                  ∴ Answer = n².

Thanks..