Question

the no.of terms of the GP sequence 3,3/2,3/4....are needed to give a sum 3069/512
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Answer 1

Answer:

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Answer 2

Given G.P is

3, (3)(1/2), (3/2)(1/2), ...

First term = 3

Common ratio = r = (1/2)

Let, number of terms in the given G.P be n.

So, sum = $\frac{a(1-r^{n}) }{1-r}$

Or, $\frac{3069}{512}=\frac{3(1-(1/2)^{n} )}{(1-(1/2))}$

Or, $\frac{1023}{1024} =1-{({\frac{1}{2}}})^{n} }$

Or, $(\frac{1}{2})^{n} = 1-\frac{1023}{1024}$

Or, $(\frac{1}{2})^{n} =\frac{1}{1024}$

Or, $2^{n} =1024$

Or, n = 10

So, number of terms in the given G.P are 10.

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