Question

In a G.P. a = 2, s4
=30 then ​

Answer 1

SOLUTION

GIVEN

$\sf{In \: a \: G.P .\: \: a = 2 \: \: and \: \: S_4 = 30}$

TO DETERMINE

The value of r

EVALUATION

Here it is given that

$\sf{In \: a \: G.P \: \: a = 2 \: \: and \: \: S_4 = 30}$

We have to find the value of r

So the first four terms are

$\sf{2 \: , \: 2r \: , \: 2 {r}^{2} \:, \:2 {r}^{3} }$

So by the given condition

$\sf{2 \: + \: 2r \: + \: 2 {r}^{2} \: + \:2 {r}^{3} = 30 }$

$\sf{ \implies \: 2(1 + r + {r}^{2} + {r}^{3} )= 30 }$

$\sf{ \implies \: (1 + r + {r}^{2} + {r}^{3} )= 15 }$

$\sf{ \implies \: (1 + r)(1 + {r}^{2} )= 15 }$

$\sf{ \implies \: (1 + r)(1 + {r}^{2} )=3 \times 5 }$

$\sf{ \implies \: (1 + r)(1 + {r}^{2} )=(1 + 2) \times (1 + {2}^{2}) }$

Which is true when r = 2

FINAL ANSWER

Hence the required value of r = 2

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