CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

If S1 be the sum of (2n + 1) terms of an A.P. and S2 be the sum of its odd terms, then prove that S1:S2=(2n+1):(n+1).


Solution

In A.P. ‘a’ be the first term and d be the common difference then
Sn=n2[2a+(n1)d]
Given that S1 be the sum of (2n + 1) terms then
S1=(2n1)2[2a+(2n+11)d]
S1=(2n1)2[2a+2(a+nd)]
S1=(2n+1)(a+nd)
S2 be the sum of its odd terms i.e.
S2=a1+a3+a5+...+a(2n1)
S2=a+(a+2d)+...+(a+2nd)
S2=(n+1)a+2n(n+1)2d
S2=(n+1)a+n(n+1)d
S2=(n+1)[a+nd]
S1:S2=(2n+1)(a+nd):(n+1)(a+nd)
S1:S2=(2n+1):(n+1)

 

flag
 Suggest corrections
thumbs-up
 
0 Upvotes


Similar questions
View More



footer-image