What is the sum of the geometric sequence -1, 6, -36, ... if there are 7 terms?

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Answer 1 · 2015-09-02T10:14:46

$S_{7} = - 39991$ $S_7=-39991$

In this sequence we have: $a_{1} = - 1$ $a_1=-1$ , $q = - 6$ $q=-6$ , $n = 7$ $n=7$ . If we apply the formula for $S_{n}$ $S_n$ we get:

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

$S_{7} = (- 1) \cdot \frac{1 + 279936}{7}$ $S_7=(-1)*(1+279936)/7$

$S_{7} = - 39991$ $S_7=-39991$

Answer 2 · 2016-08-20T12:04:53

$S_{n} = - 39, 991$ $S_n = -39,991$

In the given GP, we have the following:

$a_{1} = - 1, and n = 7$ $a_1 = -1, and n = 7$

We can find $r = \frac{6}{- 1} = - \frac{36}{6} = - 6$ $r = 6/-1 =-36/6= -6$

There are 2 formulae for $S_{n}$ $S_n$ depending on whether r is a proper fraction or not.

$S_{n} = \frac{a (r^{n} - 1)}{r - 1} substitute with the values$ $S_n = (a(r^n - 1))/(r-1)" substitute with the values"$

$S_{n} = \frac{- 1 ({(- 6)}^{7} - 1)}{- 6 - 1}$ $S_n = (-1((-6)^7 - 1))/(-6-1)$

$S_{n} = \frac{- 1 (- 279, 937)}{- 7}$ $S_n = (-1(-279,937))/(-7)$

$S_{n} = - 39, 991$ $S_n = -39,991$