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

If there are (2n+1) terms in an AP, then show that : Sum of odd termsSum of even terms=n+1n.

Open in App
Solution

Let a be the first term and d be the common difference of the given AP.
Now, sum of odd terms = S1=a1+a3+a5+.....+a2n+1

S1=n+12(a1+a2n+1)

S1=n+12[a1+a1+(2n+11)d]

S1=n+12(a+a+2nd)=(n+1)(a+nd)

Also, sum of even terms = S2=a2+a4+a6+....+a2n

S2=n2(a2+a2n)

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

S2=n2(2a+2nd)=n(a+nd)

Therefore,
S1S2=(n+1)(a+nd)n(a+nd)=n+1n

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