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.
4729
8116
27
36
Correct answer is D
The nth term of a GP is given by: Tn=arn−1.
T3=ar3−1=ar2=81.......(1)
T7=ar7−1=ar6=16 ...... (2)
Dividing (2) by (1), we have r4=1681=(23)4⟹r=23
Putting r=23 in equation (1), we have 81=a×(23^{2} = a \times \frac{4}{9} \implies a = \frac{729}{4}\)
T5=ar5−1=ar4=7294×(23)4
= 7294×1681=36
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