# What are the next three terms of the sequence 1, -3, 9, -27,…?

Aug 10, 2018

The next three terms are : 81,-243,729

#### Explanation:

The given sequence is $: 1 , - 3 , 9 , - 27 , \ldots$

$\therefore \text{First term : } {a}_{1} = 1 \mathmr{and}$

$\text{common ratio : } r = \frac{- 27}{9} = \frac{9}{- 3} = \frac{- 3}{1} = - 3$

Now ,${a}_{1} = 1 , {a}_{2} = - 3 , {a}_{3} = 9 , {a}_{4} = - 27$

So, the next three terms are :

${a}_{5} = \left({a}_{4}\right) \left(r\right) = \left(- 27\right) \left(- 3\right) = 81$

${a}_{6} = \left({a}_{5}\right) \left(r\right) = \left(81\right) \left(- 3\right) = - 243$

${a}_{7} = \left({a}_{6}\right) \left(r\right) = \left(- 243\right) \left(- 3\right) = 729$