# What is the general term of the sequence {10,-20,40,-80,....}?

Oct 26, 2016

General term of given sequence is $10 \times {\left(- 2\right)}^{n - 1}$

#### Explanation:

Here the ratio between a term and its preceding term is constant as $- \frac{20}{10} = \frac{40}{-} 20 = - \frac{80}{40} = - 2$

Hence it a geometric sequence with first term as $10$ and common ratio as $- 2$.

The general term of a geometric sequence with first term as $a$ and common ratio as $r$ is $a \times {r}^{n - 1}$.

Hence, general term of given sequence is $10 \times {\left(- 2\right)}^{n - 1}$