Danelle Albright

2022-01-07

Find S, for the geometric sequences: $4,-20,100$

kalfswors0m

Expert

The sequence has a ratio that is common to
$r=\frac{-20}{4}=-5r$
$=\frac{100}{-20}=-5$
Since, the value of the $r<1$, the formula for the sum of the n term of the series is:
${S}_{n}=\frac{a\left(1-rn\right)}{1-r}$
The total of the first five terms is then
${S}_{5}=\frac{4\left(1-\left(-5\right)\left\{5\right\}\right)}{1-\left(-5\right)}$
$=\frac{4\left(1+3125\right)}{1+5}$
$=4\frac{3126}{6}$
$=4\left(521\right)=2084$
Thus, the sum of the first five terms is 2084.

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