Evaluate s5 for 600 + 300 + 150 + …

Solution:

Given, the series is 600, 300, 150,.....

We have to find the sum upto 5 terms.

The given series is in geometric progression.

First term,a = 600

Common ratio, r = b/a = c/b

r = 300/600 = 150/300 = 1/2

So, r = 1/2

The sum of the geometric series is given by \(s_{n}=a(\frac{1-r^{n}}{1-r})\)

So, \(s_{5}=600(\frac{1-(\frac{1}{2})^{5}}{1-(\frac{1}{2})})\)

\(s_{5}=600(\frac{1-(\frac{1}{32})}{\frac{1}{2}})\)

\(s_{5}=600(\frac{\frac{31}{32}}{\frac{1}{2}})\)

\(s_{5}=600({\frac{31\times 2}{32}})\)

\(s_{5}=600({\frac{31}{16}})\)

\(s_{5}=150({\frac{31}{4}})\)

\(s_{5}=1162.5\)

Therefore, \(s_{5}=1162.5\).

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Evaluate s5 for 600 + 300 + 150 + …

Summary:

Evaluating the sum of series 600, 300, 150,...upto 5 terms is \(s_{5}=1162.5\).