What is the sum of the first eight terms of the series?

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What is the sum of the first eight terms of the series?

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Answer 1 · 2018-04-16T10:30:54

-625

Explanation:

We have a geometric series which follows $a_{n} = a r^{n - 1}$ $a_n =ar^(n-1)$

$a = first term = - 500$ $a="first term"=-500$
$r = common ratio = \frac{a_{2}}{a_{2}} = - \frac{100}{- 500} = \frac{1}{5}$ $r="common ratio"=a_2/a_2=-100/-500=1/5$

Sum of a geometric series is given by:
$S_{n} = a_{1} (\frac{1 - r^{n}}{1 - r})$ $S_n=a_1((1-r^n)/(1-r))$

$S_{8} = - 500 (\frac{1 - {0.2}^{8}}{1 - 0.2}) = - 55 (\frac{0.99999744}{0.8}) = - 500 (1.2499968) = - 624.9984 \approx - 625$ $S_8=-500((1-0.2^8)/(1-0.2))=-55(0.99999744/0.8)=-500(1.2499968)=-624.9984~~-625$

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What is the sum of the first eight terms of the series?

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