Question

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

Answer 1

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,

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

Answer 2

The sum of the first five terms of the geometric progression 600 + 300 + 150 + …  is 1162.5.

What is the ratio of geometric progression?

A geometric progression is the series of numbers where the ratio of the two consecutive numbers is always the same.

As it is given to us the sequence 600, 300, 150 is a geometric progression. Therefore, the first term of the progression is 600, while the ratio between the two terms are,

$r = \dfrac{300}{600} = \dfrac{1}{2}$

Now,  we know that the sum of the geometric sequence of the first 5 terms can be written as where the value of the n is 5,

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

$S=600\dfrac{(1-(\dfrac{1}{2})^n)}{(1-(\dfrac{1}{2}))}$

$S = 1162.5$

Hence, the sum of the first five terms of the geometric progression 600 + 300 + 150 + …  is 1162.5.

Learn more about Geometric Progression:

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