How do you find the sum of the infinite geometric series 72 + 12 + 2 + +… ?

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How do you find the sum of the infinite geometric series 72 + 12 + 2 + +… ?

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Answer 1 · 2016-01-10T20:42:27

$\frac{432}{5} = 84 \frac{2}{5}$ $432/5 = 84 2/5$

Explanation:

The formula for the sum of an infinite series is $S = \frac{a}{1 - r}$ $S = a/(1-r)$
where r is the common ratio and a is the first term.

Therefore, $S = \frac{72}{1 - \frac{1}{6}} = \frac{72}{\frac{5}{6}} = \frac{432}{5}$ $S = 72/(1-1/6)=72/(5/6)=432/5$

Answer 2 · 2016-01-10T20:42:29

First, you must find the common ratio, r, of the series.

Explanation:

r = $\frac{t_{2}}{t_{1}}$ $t_2 / t_1$

r = $\frac{12}{72}$ $12/72$

r = $\frac{1}{6}$ $1/6$

$S_{\infty}$ $S_∞$ = $\frac{a}{1 - r}$ $a/(1 - r)$

$S_{\infty}$ $S_∞$ = $\frac{72}{1 - \frac{1}{6}}$ $72/(1 - 1/6)$

$S_{\infty}$ $S_∞$ = $\frac{72}{\frac{5}{6}}$ $72/(5/6)$

$S_{\infty}$ $S_∞$ = $\frac{72 ∙ 6}{5}$ $(72 • 6)/ 5$

$S_{\infty}$ $S_∞$ = $\frac{432}{5}$ $432/5$ or 146.4

The sum is $\frac{432}{5}$ $432/5$ or 146.4. Hopefully you understand now!

Below I have posted one problem for your practice.

Find the wanted information.

a) An infinite geometric series has a third term of 18 and a common ratio of $\frac{1}{2}$ $1/2$ . Find it's sum.

b) A pendulum has a first swing of 186 centimeters and a second swing of 124 centimetres. Assuming the pendulum swings forever, find the total distance travelled, rounded to the closest hundredth when necessary.

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How do you find the sum of the infinite geometric series 72 + 12 + 2 + +… ?

2 Answers

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