Question

If in an A.P S7=49 and S17=289 than sn..

Answer 1

Step-by-step explanation:

Givrn:

S7=> 7/2(2a+(7-1)d)=49.

=> 14a+42d/2=49

=> 7a+21d=49

=> 7(a+3d}=49

=> a+3d=7.------(1)

S17=> 17/2(2a+(17-1)d)=289.

=> 34a+272d/2=289

=> 17a+136d=289

=> 17(a+8d)=289

=> a+8d=17.-----(2)

By (2)-(1):

=> a+8d-(a+3d)=17-7

=> a+8d-a-3d=10

=> 5d=10

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

Sn=n/2(2×1+(n-1)×2)

=> n/2(2+2n-2)

=> n×2/2(1+n-1)

=> n×n

Sn=n².

=> d=10/5=2-----(3).

(3) in (1):

=> a+3(2)=7.

=> a=7-6=1.