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

Sep 2, 2015

${S}_{7} = - 39991$

#### Explanation:

In this sequence we have: ${a}_{1} = - 1$, $q = - 6$, $n = 7$. If we apply the formula for ${S}_{n}$ we get:

${S}_{7} = \left(- 1\right) \cdot \frac{1 - {\left(- 6\right)}^{7}}{1 - \left(- 6\right)}$

${S}_{7} = \left(- 1\right) \cdot \frac{1 + 279936}{7}$

${S}_{7} = - 39991$

Aug 20, 2016

${S}_{n} = - 39 , 991$

#### Explanation:

In the given GP, we have the following:

${a}_{1} = - 1 , \mathmr{and} n = 7$

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

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

${S}_{n} = \frac{a \left({r}^{n} - 1\right)}{r - 1} \text{ substitute with the values}$

${S}_{n} = \frac{- 1 \left({\left(- 6\right)}^{7} - 1\right)}{- 6 - 1}$

${S}_{n} = \frac{- 1 \left({\left(- 6\right)}^{7} - 1\right)}{- 6 - 1}$

${S}_{n} = \frac{- 1 \left(- 279 , 937\right)}{- 7}$

${S}_{n} = - 39 , 991$