Question

If the third term of G.P. is 10 . Then the product of the first five terms of G.P. is :​

Answer 1

$\underline{\boxed{\bold{Question}}}$  

↠ If the third term of G.P. is 10 , Then the product of the first five terms of G.P. is = ?

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$\underline{\boxed{\bold{Important\;Information}}}$  

❏ G.P. is a sequence of non zero numbers each of the succeeding term is equal to the preceding term multiplied  by a constant.

❏ Thus in a GP the ratio of successive terms is constant. This constant factor is called the COMMON  RATIO of the sequence & is obtained by dividing any term by the immediately previous term.

❏ Therefore a, ar,  ar², ar³, ar⁴ , .......... is a GP with 'a' as the first term & 'r' as common ratio.

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$\underline{\boxed{\bold{Given}}}$

↠ Third term = 10

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$\underline{\boxed{\bold{Answer}}}$

Let's Start !

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Let's the GP be as follow :

 

↠ a, ar,  ar², ar³, ar⁴ are in GP where :

❏ a     ➡️ First term

❏ ar   ➡️ Second term

❏ ar²  ➡️ Third term

❏ ar³  ➡️ Fourth term

❏ ar⁴  ➡️ Fifth term

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$\boxed{\bold{\red{\therefore Product \ of \ terms = P = a \times ar \times ar^2 \times ar^3 \times ar^4 }}}$

$:\implies P = a \times ar \times ar^2 \times ar^3 \times ar^4$

$:\implies P = a^5 r^{10}$

$:\implies P = (ar^2)^5$

$:\implies P = (Third \; term)^5$

$\boxed{\bold{\blue{:\implies P = (10)^5 = 1,00,000 }}}$

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$\boxed{\boxed{\bold{\blue{\therefore Product \; of \; 5 \; terms\;of\;GP =  (10)^5 = 1,00,000 }}}}$

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Hope this helps u.../

【Brainly Advisor】

Answer 2

$\underline{\boxed{\bold{\orange{Question}}}}$

↠ If the third term of G.P. is 10 , Then the product of the first five terms of G.P. is = ?

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$\underline{\boxed{\bold{\orange{Important\;Information}}}}$

❏ G.P. is a sequence of non zero numbers each of the succeeding term is equal to the preceding term multiplied  by a constant.

❏ Thus in a GP the ratio of successive terms is constant. This constant factor is called the COMMON  RATIO of the sequence & is obtained by dividing any term by the immediately previous term.

❏ Therefore a, ar,  ar², ar³, ar⁴ , .......... is a GP with 'a' as the first term & 'r' as common ratio.

━━━━━━━━━━━━━━━━━━━━━━━━━━

$\underline{\boxed{\bold{\orange{Given}}}}$

↠ Third term = 10

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$\underline{\boxed{\bold{\orange{Answer}}}}$

Let's Start !

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Let's the GP be as follow :

 

↠ a, ar,  ar², ar³, ar⁴ are in GP where :

• a     ➡️ First term

• ar   ➡️ Second term

• ar²  ➡️ Third term

• ar³  ➡️ Fourth term

• ar⁴  ➡️ Fifth term

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$\boxed{\bold{\red{\therefore Product \ of \ terms = P = a \times ar \times ar^2 \times ar^3 \times ar^4 }}}$

$:\implies P = a \times ar \times ar^2 \times ar^3 \times ar^4$

$:\implies P = a^5 r^{10}$

$:\implies P = (ar^2)^5$

$:\implies P = (Third \; term)^5$

$\boxed{\bold{\blue{:\implies P = (10)^5 = 1,00,000 }}}$

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$\boxed{\boxed{\bold{\blue{\therefore Product \; of \; 5 \; terms\;of\;GP =  (10)^5 = 1,00,000 }}}}$

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