wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

a1,a2,a3,.....,an are in an A.P.
1a1+a2+1a2+a3+...+1an1+an=(n1)an+a1

Open in App
Solution

1a1+a2+1a2+a3+....+1an1+an
Let S be the Sum and d be the common difference
S=1a2+a1+1a3+a2+....+1an+an1
Rationalising each term, we get
S=1a2+a1+1a3+a2+....+1an+an1S=a2a1a2a1+a3a2a3a2+a4a3a4a3+...+anan1anan1S=a2a1d+a3a2d+a4a3d+...+anan1dS=ana1d×an+a1an+a1=ana1d(an+a1)(1)an=a1+(n1)dana1=(n1)d(2)From(1)and(2)S=ana1d(an+a1)=(n1)dd(an+a1)=(n1)(an+a1)

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Arithmetic Progression - Sum of n Terms
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon