Question

5. Find the sum of the first 8 terms of Geometric Progression whose first term a= 1 common ratio r =2​

Answer 1

Answer:

Given, a

1

=2,r=2

S

n

=

r−1

a

1

(r

n

−1)

S

8

=

2−1

2(2

8

−1)

=

1

2(255)

=510

Answer 2

Given,

$\[\begin{array}{l}a = 1\\r = 2\end{array}\]$

Solution,

Formula used,$\[{S_n} = \frac{{a\left( {{r^n} - 1} \right)}}{{r - 1}}\]$

Apply values.

$\[\begin{array}{l} \Rightarrow \frac{{1\left( {{2^8} - 1} \right)}}{{2 - 1}}\\ \Rightarrow \frac{{1\left( {{2^8} - 1} \right)}}{1}\\ \Rightarrow 256 - 1\\ \Rightarrow 255\end{array}\]$

Hence, the sum of the first eight terms of the series is$\[255\].$