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Question

Mathematics Question on Sequence and series

If the third term of a G.P. is 3, then the product of its first 5 terms is

A

15

B

81

C

243

D

Cannot be determined.

Answer

243

Explanation

Solution

T3=ar2=3T_{3} = ar^{2} = 3 Product of first five terms =aarar2,ar3ar4= a\cdot ar\cdot ar^{2} , ar^{3}\cdot ar^{4} =a5r10=(ar2)5=(3)5= a^{5}\cdot r^{10} = \left(ar^{2}\right)^{5} = \left(3\right)^{5} =243= 243