Let a, b, c, d and e be distinct positive number. If a, b, c and $$1c$$,$$1d$$,$$1eboth$$ are in A.P. and b, c, d are in G.P. then

Correct option is 4a, c, e are in G.P

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Let $a, b, c, d$ and $e$ be distinct positive number. If $a, b, c$ and $\frac{1}{c}, \frac{1}{d}, \frac{1}{e}$ both are in A.P. and $b, c, d$ are in G.P. then

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detailed solution

Correct option is D

2b=a+c,2d=1c+1e,c2=bdNow, 2cec+e=d=c2b⇒ec+e=c2b=ca+c⇒ae+ce=c2+ce⇒c2=ae⇒a,c,e are in G.P.

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Let a, b, c, d and e be distinct positive number. If a, b, c and 1c,1d,1eboth are in A.P. and b, c, d are in G.P. then

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Let $a, b, c, d$ and $e$ be distinct positive number. If $a, b, c$ and $\frac{1}{c}, \frac{1}{d}, \frac{1}{e}$ both are in A.P. and $b, c, d$ are in G.P. then