Question

find the sum of the first five terms of a geometric sequence whose first term is 128 and common ratio is 1/2.

Answer 1

ANSWER

Given that eighth term of a G.P is 128

=> a×r

8−1

=128

also given common ratio, r=2

Thus, we obtain first term a=1 from first equation

so the product of first 5 terms 1,r,r

2

,r

3

,r

4

=r

10

=2

10

=4

5

Answer 2

Given:

The first term of a geometric sequence is 128

Common ratio is $\frac{1}{2}$

To find :

The sum of the first five terms of a geometric sequence.

Formula to be used:

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

Solution:

We can find the sum of the first five terms of a geometric sequence by using the following formula,

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

Here, n = 5 , a = 128 and r =  $\frac{1}{2}$

$S_5 =\frac{128((\frac{1}{2} )^5-1)}{\frac{1}{2} -1}$

$S_5 =\frac{128(\frac{1}{32} -1)}{\frac{1-2}{2} }$

$S_5 =\frac{128(\frac{1-32}{32})}{\frac{-1}{2} }$

$S_5 =4(-31)$ × $(\frac{-2}{1} )$

$S_5 =248$

Final answer:

The sum of the first five terms of a geometric sequence is 248