What is the sum of the geometric sequence -3, 18, -108, … if there are 7 terms?

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What is the sum of the geometric sequence -3, 18, -108, … if there are 7 terms?

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Answer 1 · 2018-08-14T19:59:33

$S_{7} = - 119973$ $S_7=-119973$

Explanation:

$the sum to n terms for a geometric sequence is$ $"the sum to n terms for a geometric sequence is"$

$∙ x S_{n} = \frac{a (r^{n - 1})}{r - 1}$ $•color(white)(x)S_n=(a(r^(n-1)))/(r-1)$

$where a is the first term and r the common ratio$ $"where a is the first term and r the common ratio"$

$a = - 3 and r = \frac{- 108}{18} = \frac{18}{- 3} = - 6$ $a=-3" and "r=(-108)/18=18/(-3)=-6$

$S_{7} = \frac{- 3 ({(- 6)}^{7} - 1)}{- 6 - 1}$ $S_7=(-3((-6)^7-1))/(-6-1)$

$\times = \frac{- 3 (- 279936 - 1)}{- 7}$ $color(white)(xx)=(-3(-279936-1))/(-7)$

$\times = \frac{- 3 \times - 279937}{- 7} = - 19973$ $color(white)(xx)=(-3xx-279937)/(-7)=-19973$

Answer 2 · 2018-08-14T20:01:07

$S_{7} = - 119973$ $S_7=-119973$

Explanation:

Here,

$-3,18,-108,..."are in GP"$

Let ,first term $=a_1=-3 and$

common ratio $=r=(-108)/18=18/(-3)=-6$

So, the sum of first n terms is:

$S_n=(a_1(1-r^n))/(1-r) ,where, n=7$

$:S_7=(-3(1-(-6)^7))/(1-(-6))$

$:.S_7=-(3(1+279936))/7=-(3(279937))/7=-119973$

Answer 3 · 2018-08-14T20:01:09

-119973

Explanation:

We can first see that the ratio between these is $-6$ . This means we have the sum of a geometric series, which we know is
$S_n = a_1 * (r^n-1)/(r-1) = -3 * ((-6)^7 - 1)/((-6)-1) = -119973$

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What is the sum of the geometric sequence -3, 18, -108, … if there are 7 terms?

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