#### Question

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.

#### 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.

Is there an error in this question or solution?

Solution 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 Geometric Progression Concept: Geometric Progression (G. P.).