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

The sums of first n terms of three arithmetic progressions are S1, S2 and S3 respectively. The first term of each A.P. is 1 and their common difference are 1, 2 and 3 respectively. Prove that S1+S3=2S2.

Open in App
Solution

Given, first term of each A.P. (a)=1.

and their common difference are 1,2 and 3.

S1=n2[2a+(n1)d1]

= n2(2+(n1)1)=n2(n+1)

S2=n2[2a+(n1)d2]

= n2(2+(n1)2)=n2(2n)=n2

and S3=n2[2a+(n1)d3]

= n2(2+(n1)3)=n2(3n1)

Now, S1+S3=n2(n+1)+n2(3n1)

= n2(n+1+3n1)=4n×n2=2n2

= 2S2

S1+S3=2S2

Hence Proved.


flag
Suggest Corrections
thumbs-up
62
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
General Form of an AP
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon