Question

the third term of a gp is 10
the product of the first 5 term is 1000 10000 100 100000​

Answer 1

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

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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LEARN MORE FROM BRAINLY

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

https://brainly.in/question/24023437

Answer 2

$Let \: 'a' \:and \: 'r' \: are \: first \:term \: and \\common \: ratio \: of \: a \: G.P$

/* We know that */

$\boxed{\pink{ n^{th}\: term (a_{n}) = ar^{n-1} }}$

$Third \: term (a_{3} ) = 10 \: (given)$

$\implies ar^{2} = 10 \: ---(1)$

$\blue{ Product \: of \: the \: first \: 5 \: terms }$

$= a \times ar \times ar^{2} \times ar^{3} \times ar^{4} \\= a^{5} \times r^{10} \\= a^{5} \times (r^{2})^{5} \\= (ar^{2})^{5} \\= 10^{5} \: [From \: (1) ]$

$= 100000$

Therefore.,

$\red{ Product \: of \: the \: first \: 5 \: terms }$

$\green {= 100000}$

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