Question

Sum of 7terms of an a.p is 49 ;17 termis289 find sum of n terms

Answer 1

S7=7/2(2a+(7-1)d)
=>49=7/2(2a+6d)
=>49=14/2a+42/2d
=>49=7a+21d
=>49=7(a+3d)
=>49/7=a+3d
=>a+3d=7. ...............[1]

S17=17/2$#(2a+(17-1)d)
=>289=34/2a+(16*17)/2d
=>289=17a+136d
=>17a+136d=289
.=>17(a+8d)=289
=>a+8d=289/17
=>a+8d=17...................[2]

Subtracting (1 ) from ( 2)
a+8d=17
a+3d=7
- - = -
........................
5d=10
=>d=2
On substitute the value of d we get
a=1

Now
Sn=n/2(2a+(n-1)d)
Sn=n/2(2*1+(n-1)2)
Sn=n/2(2+2n-2)
Sn=n/2*2(1+n-1)
Sn=n*n
Sn=n²