CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
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.

Open in App
Solution

Given
S7=49 and S17=289

By using Sn=n2[2a+(n1)d] we have,


S7=72[2a+(71)d]=49

49=72[2a+(71)d]

49=72(2a+6d)

7=a+3d

a+3d=7...................(i)

S17=172[2a+(171)d]=289

289=172[2a+(171)d]

289=172(2a+16d)

17=a+8d

a+8d=17......................(ii)

Substituting (i) from (ii), we get

5d=10 or d=2

From equation (i),

a+3(2)=7

a+6=7 or a=1

Sn=n2[2(1)+(n1)2]

=n2[2+(n1)2]

=n2(2+2n2)=n2

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
General term of an AP
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon