How do you find the sum of the infinite geometric series a1= 343, r=7, and a4= -1?

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Answer 1 · 2016-03-21T10:10:42

$S = 300.125$ $S=300.125$

For what I can see from the problem. The number sequence may probably be like as follows;

343 -49 7 -1

in this case, $r = - \frac{1}{7}$ $r= -1/7$

and $a_{1} = 343$ $a_1=343$ and $a_{4} = - 1$ $a_4=-1$

The formula for Sum of infinite geometric series with $0$ $0$ < $r$ $r$ < $1$ $1$ is

$S = \frac{a_{1}}{1 - r}$ $S=a_1/(1-r)$

$S = \frac{343}{1 - - \frac{1}{7}} = \frac{343}{\frac{8}{7}} = \frac{2401}{8} = 300.125$ $S=343/(1--1/7)=343/(8/7)=2401/8=300.125$

God bless....I hope the explanation is useful.