Question

The third term of G.P. is 10. Then the product of first five terms is (a) 1000 (b) 10000 (c) 100 (d) 100000​

Answer 1

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GIVEN

The third term of a Geometric Progression is 10

TO CHOOSE THE CORRECT OPTION

The product of the first 5 term is

1000

10000

100

100000

CALCULATION

Let the first five terms of the Geometric Progression is

$\displaystyle \sf{ \frac{a}{ {r}^{2} } \: , \: \frac{a}{r} \:, \: a \: , \: ar \:, \: a {r}^{2} \: \: }$

By the given condition

Third term of the Geometric Progression = a = 10

Hence the product of the first 5 term is

$= \displaystyle \sf{ \frac{a}{ {r}^{2} } \: \times \: \frac{a}{r} \times \: a \ \times \: ar \times \: a {r}^{2} \: \: }$

$= \sf{ {a}^{5} \: }$

$\sf{ = {10}^{5} \: }$

$= \sf{100000 \: }$

RESULT

The product of the first 5 term is 100000

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The product of three geometric means between 5 and 125 will be (a) 3125 (b) 15625 (c) 125 (d) 625

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