# 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 - Mathematics

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 abc are in A.P.

∴ b – a = c – b … (1)

It is given that bcd, are in G.P.

∴ c2 = bd … (2)

Also   1/c, 1/d,1/e are in A.P.

Thus, ac, and e are in G.P.

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#### APPEARS IN

NCERT Class 11 Mathematics Textbook
Chapter 9 Sequences and Series
Q 20 | Page 200