# What is the fifteenth term of the sequence 5,-10,20,-40,80?

${a}_{15} = 81920$

#### Explanation:

from the given set of numbers 5,-10,20,-40,80...it appears like Geometric Sequence and with first term ${a}_{1} = 5$ and the common ratio $r = \frac{80}{- 40} = \frac{- 40}{20} = \frac{20}{- 10} = \frac{- 10}{5} = - 2$

$r = - 2$

the formula to find the $n t h$ term in Geometric Progression is

${a}_{n} = {a}_{1} \cdot {r}^{n - 1}$

Use now ${a}_{1} = 5$ and $r = - 2$ and $n = 15$ in the formula

${a}_{n} = {a}_{1} \cdot {r}^{n - 1}$

${a}_{15} = 5 \cdot {\left(- 2\right)}^{15 - 1}$

${a}_{15} = 5 \cdot {\left(- 2\right)}^{14}$

${a}_{15} = 5 \cdot 16384$

${a}_{15} = 81920 \text{ " }$the 15th term

A long check helps after all there are only 15 numbers

5, -10, 20, -40, 80, -160, 320, -640, 1280, -2560, 5120, -10240, 20480, -40960, 81920

God bless....I hope the explanation is useful...