Question

The sum of n terms of a G.P. whose first terms 1 and the common ratio is 1/2, is equal to 255/128. The value of n is

Answer 1

Answer:

Value of n = 8 .

Step-by-step explanation:

We are given first term of G.P. , a = 1  and common ratio,  = 0.5 and also sum of n terms of G.P. = 255/128

Sum of n terms of GP formula is given by;

                $S_n = \frac{a(1-r^{n}) }{1-r}$    where r < 1 .

Putting above values we get,

             ⇒    $\frac{255}{128} = \frac{1(1-0.5^{n}) }{1-0.5}$  

             ⇒   $1 - 0.5^{n} = \frac{255}{128} * \frac{1}{2}$

             ⇒   $1 - 0.5^{n} = \frac{255}{256}$  

             ⇒  $(\frac{1}{2} )^{n} = 1 - \frac{255}{256}$      ⇒  $\frac{1}{2^{n} } = \frac{1}{256}$

                                               ⇒ $\frac{1}{2^{n} } = \frac{1}{2^{8} }$

So, comparing both sides we observe that n = 8.

Answer 2

Answer:

8

Step-by-step explanation:

Click on above photo

Hope it will help

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