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# Please help! - Let be a G.P. Ifthen equals : - Sequence and series - JEE Main

Let $a_{1},a_{2},...........,a_{10}$  be a G.P. If  $\frac{a_{3}}{a_{1}}=25,$ then   $\frac{a_{9}}{a_{5}}$    equals :

• Option 1)

$4(5^{2})$

• Option 2)

$5^{4}$

• Option 3)

$2(5^{2})$

• Option 4)

$5^{3}$

Views

Geometric Progession (GP) -

A progression of non - zero terms, in which every term bears to the preceding term a constant ratio.

- wherein

eg 2, 4, 8, 16,- - - - - -

and

100, 10, 1, 1/10,- - - - - - -

General term of a GP -

$T_{n}= ar^{n-1}$

- wherein

$a\rightarrow$ first term

$r\rightarrow$ common ratio

Let first term of G.D be a and common ratio = r

$a_n=ar^{n-1}$

$\frac{a_3}{a_1}=\frac{ar^{2}}{a}=25\Rightarrow r^{2}=25$

Now, $\frac{a_9}{a_5}=\frac{ar^{8}}{ar^{4}}=r^{4}=\left ( 25 \right )^{2}=5^{4}$

Option 1)

$4(5^{2})$

Option 2)

$5^{4}$

Option 3)

$2(5^{2})$

Option 4)

$5^{3}$

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