If *a, b, c* are in A.P*,*;* b, c, d* are in G.P and ` 1/c, 1/d,1/e` are in A.P. prove that *a*,* c*,* e* are in G.P.

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#### Solution

It is given that *a*, *b*, *c* are in A.P.

∴ *b* – *a* = *c* – *b* … (1)

It is given that *b*, *c*, *d*, are in G.P.

∴ *c*^{2} = *bd *… (2)

Also ` 1/c, 1/d,1/e` are in A.P.

Thus, *a*, *c*, and *e* are in G.P.

Concept: Geometric Progression (G. P.)

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