What is the sum of the geometric sequence 8, –16, 32 … if there are 15 terms?

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What is the sum of the geometric sequence 8, –16, 32 … if there are 15 terms?

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Answer 1 · 2015-11-26T16:08:02

$- 87378.66 ¯ 6$ $-87378.66bar6$

Explanation:

The sum of an $n$ $n$ term geometric sequence with initial term $a_{0}$ $a_0$ and ratio $r$ $r$ (i.e. $a_{i} = a_{i - 1} \cdot r$ $a_i=a_(i-1)*r$ )
is given by the equation:
$XXX n - 1 \sum i = 0 a_{i} = \frac{a_{0} \cdot {(1 + r)}^{n}}{1 - r}$ $color(white)("XXX")sum_(i=0)^(n-1)a_i = (a_0*(1+r)^n)/(1-r)$

In this case $a_{0} = 8$ $a_0 = 8$ and $r = (- 2)$ $r=(-2)$

So the sum is
$XXX = \frac{8 \cdot (1 + {(- 2)}^{15})}{1 - (- 2)}$ $color(white)("XXX")=(8*(1+(-2)^15))/(1-(-2))$

$XXX = \frac{8 \cdot (1 + (- 32768))}{3}$ $color(white)("XXX")=(8*(1+(-32768)))/3$

$XXX = \frac{8 \cdot (- 32767)}{3}$ $color(white)("XXX")=(8*(-32767))/3$

$XXX = \frac{- 262136}{3}$ $color(white)("XXX")=(-262136)/3$

$XXX = - (87378 \frac{2}{3})$ $color(white)("XXX")=-(87378 2/3)$

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What is the sum of the geometric sequence 8, –16, 32 … if there are 15 terms?

1 Answer

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