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Dear Chandrakesh Shukla
given
(an +bn)/(an-1 +bn-1) =(a+b)/2
2(an +bn) = (an +bn) + abn-1 + ban-1
(an +bn) = abn-1 + ban-1
an-1 (a-b) + bn-1 ( b-a)=0
(an-1 -bn-1)(a-b)=0
(an-1 +bn-1)=0
(a/b)n-1 =1
n-1 =0
n=1
Please feel free to post as many doubts on our discussion forum as you can.If you find any question Difficult to understand - post it here and we will get you the answer and detailed solution very quickly. We are all IITians and here to help you in your IIT JEE preparation.All the best. Regards,Askiitians ExpertsBadiuddin
Dear Chandrakesh
let the series has n term and the first term is =a
and comon difference is =d
now find the rth term from the biginning = a+(r-1)d
as we know rth term from the end = (n-r+1)th term from the bigining
so rth term from the end = a+(n-r+1-1)d
=a+(n-r)d
sum of rth term from the beginning and end is = a+(r-1)d +a+(n-r)d
= 2a +(n-1)d
this term is independent of r so it is a constant
Please feel free to post as many doubts on our discussion forum as you can.If you find any question Difficult to understand - post it here and we will get you the answer and detailed solution very quickly. We are all IITians and here to help you in your IIT JEE preparation. All the best. Regards,Askiitians ExpertsBadiuddin
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