if an +bn /an-1 +bn-1 is a G M between a and b, then the value of n is - Maths - Sequences and Series

Question

if an +bn /an-1 +bn-1
is a G M between a and b, then the value of n is?

Rahul Raj · Accepted Answer

dear student

for the terms to be in GPan+bnan-1+bn-1=aban+bn=(an-1+bn-1)aban+bn=an-1/2b+bn-1/2aan-an-1/2b+bn-bn-1/2a=0an-1/2a-b-bn-1/2a-b=0a-ban-1/2-bn-1/2=0but a is not equal to bso, an-1/2-bn-1/2=0only when n-1/2=0n=1/2

regards

if an +bn /an-1 +bn-1 is a G.M. between a and b, then the value of n is?

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