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

Answer 1

given ,
S7=49
S17=289
S7=7/2[2a+(n-1)d]
S7=7/2[2a+(7-1)d]
49=7/2(a+16d)
7=(a+3d)
a+3d=7...(i)
similarly,
S17=17/2[2a+(17-1)d]
289=17/2[2a+(16)d]
17=(a+8d)
a+8d=17...(ii)
subtacting equation (i) freom(ii),
5d=10
d=2
from equation (i),
a+3(2)=7
a+6=7
a=1
Sn=n/2[2a+(n-1)d]
     =n/2[21+(n-1)2]
     =n/2(2+2n-2)
     = n/2(2n)
    Sn =n2