Question

In a G.p a=v5,r=2v5 find T5​

Answer 1

Answer:

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Answer 2

SOLUTION

GIVEN

In a GP

$\sf{a = \sqrt{5} \: ,\: r = 2 \sqrt{5} }$

TO DETERMINE

$\sf{ t_5 }$

CONCEPT TO BE IMPLEMENTED

If in a Geometric Progression

First term = a and common ratio = r

Then n th term

$\sf{ t_n = a \times {r}^{n - 1} }$

EVALUATION

Here it is given that

First term = a = √5

Common Ratio = r = 2√5

Hence 5 th term

$\sf{ = t_5 }$

$\sf{ = \sqrt{5} \times {(2 \sqrt{5}) }^{5 - 1} }$

$\sf{ = \sqrt{5} \times {(2 \sqrt{5}) }^{4} }$

$\sf{ = \sqrt{5} \times 16 \times 5 \times 5 }$

$\sf{ = 400 \sqrt{5} }$

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