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The 3rd and 7th term of a Geometric Progression (GP) are ...

The 3rd and 7th term of a Geometric Progression (GP) are 81 and 16. Find the 5th term.

A.

4729

B.

8116

C.

27

D.

36

Correct answer is D

The nth term of a GP is given by: Tn=arn1.

T3=ar31=ar2=81.......(1)

T7=ar71=ar6=16 ...... (2)

Dividing (2) by (1), we have r4=1681=(23)4r=23

Putting r=23 in equation (1), we have 81=a×(23^{2} = a \times \frac{4}{9} \implies a = \frac{729}{4}\)

T5=ar51=ar4=7294×(23)4

= 7294×1681=36