Question

133. Ifa, a,.ag....... den bare in A.P and a.... ...... B.. b are in G.P and C is the H.Mofa and b then a, + 2 + B.Ban B2B B.B.. Is equal to (D) (A) 2n/C (B) (C) 2nc C/2n O ,

JEE/Engineering Exams

Maths

Solution

125

4.0 (1 ratings)

( a quad alpha, alpha_{2} quad alpha_{3} ldots quad alpha_{2 n}, b quad ) in ( quad A P ) ( alpha_{i}=a+i d . quad, quad b=a+(2 n+1) d ) ( begin{aligned} text { and } a+b=alpha_{1}+alpha_{2 n}=& alpha_{2}+alpha_{2 n-1}=ldots & text { an let it } b_{c} quad dot{alpha} end{aligned} ) ( a quad B, beta_{2}, quad B_{3} ) ( B_{2 n}, b_{n} ) ( Q P ) ( B i=a x^{i} quad, quad b=a lambda^{2 n+1} ) ( a cdot b=beta, B_{2 n}=B_{2} B_{2 n-1}=begin{array}{c}B_{3} B_{2 n-2} a_{n} d text { let it } b_{e} betaend{array} ) ( c=frac{2 a b}{a+b} ) ( frac{alpha_{1}+alpha_{n}}{beta_{1} beta_{22}}+frac{alpha_{2}+alpha_{2 n}}{B_{2} B_{2 n}-1} ldots quad=nleft(frac{alpha}{beta}right)=nleft(frac{a+b}{a_{b}}right) ) ( Rightarrow y=frac{n times 2}{c}=frac{2 n}{c} )