Question

Evaluate S5 for 600 + 300 + 150 + … and select the correct answer below

Answer 1

The anwser is A 1162.5.

Answer 2

Answer:

Hence,

$S_5=1162.5$

Step-by-step explanation:

We are asked to evaluate:

$S_5$

We are given a geometric series.

( since each term of the series are in geometric progression as each term is half of the previous term of the series.

i.e. we have a common ratio of 1/2 )

Also, we know that sum of n terms in geometric progression is given by:

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

where r is the common ratio.

a is the first term of the series.

Here we have:

$a=600\ ,\ r=\dfrac{1}{2}$

Hence,

$S_5=600(\dfrac{1-(\dfrac{1}{2})^5}{1-\dfrac{1}{2}})\\\\\\S_5=600(\dfrac{2^5-1}{2^4}})\\\\\\S_5=600(\dfrac{31}{16})\\\\\\S_5=1162.5$