Question

If the sum of first 7 terms of an ap is 49 and that of first seventeen terms is 289 then find the sum of first n terms.

Answer 1

Answer:

Step-by-step explanation:

Let a is first term and d= cd

Then S7=7/2(2a+6d)=49

2a+6d=49*2/7=14

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

S17=17/2(2a+16d)=289

2a+16d=289*2/17=17*2=34

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

subtracting (1) from(2)

5d=10,d=2

from(1)

a+3*2=7

a=7-6=1

So Sn=n/2(2*1+(n-1)*2)

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

=n/2*2n=n²

So sum of n terms = n²