Question

If the sum of first 7 terms of an AP is 49 and that of 17 terms is 289 ,then find the sum of first n terms?

Answer 1

a7=49
a+6d=49. (1)


a17=289.
a+16d=289. (2)



subtracting (1) and (2)

a+6d=49
a+16d=289
- - -
_________
-10d=-240



d=24

therefore,
a=49-(6*24)
a=49-144



a=-95


sum of first n term(sn)=n/2(2a+(n-1)d)
sn=n/2(2(-95)+(n-1)24)
=n/2(-190+24n-24)
=n/2(24n-214)
=n/2*2(12n-57)
=n(12n-57)

sn=12n^2-57 (answer)