Question

If the sum of first7 th term of an AP is 49 and that of 17 term is 289 find the sum of first n term

Answer 1

here sum formula Sn=n/2[2a+(n-1)d]
when S7=7/2[2a+(7-1)d]
I.e 49=7/2[2a+6d]
7=1/2(2a+6d)
7=a+3d..... (1)
Sn=n/2(2a+(n-1)d
289=17/2(2a+(17-1)d
17=1/2(2a+16d)
17=a+8d....... (2)
Subtracting eq 1 and eq 2
a+3d=7
a+8d=17
(-). (-). (-)
-5d=-10
d=2
putting the value of d in eq 1
a+3d=7
a+3×2=7
a=1
Sn=n/2(2a+(n-1)d
=n/2(2×1+(n-1)2
=n/2(2+2n-2)
=n/2×2n ( cancel 2)
=n×n
=n2