# How do you write the first five terms of the geometric sequence a_1=2, r=3?

Feb 16, 2017

First five terms of geometric sequence are $\left\{2 , 6 , 18 , 54 , 162\right\}$

#### Explanation:

In a geometric sequence if ${a}_{1}$ is the first term and common ratio is $r$,

then the ${n}^{t h}$ term ${a}_{n}$ is given by ${a}_{n} = {a}_{1} {r}^{\left(n - 1\right)}$

Here ${a}_{1} = 2$ and $r = 3$

hence ${a}_{2} = 2 \times {3}^{\left(2 - 1\right)} = 2 \times {3}^{1} = 2 \times 3 = 6$,

${a}_{3} = 2 \times {3}^{\left(3 - 1\right)} = 2 \times {3}^{2} = 2 \times 9 = 18$,

${a}_{4} = 2 \times {3}^{\left(4 - 1\right)} = 2 \times {3}^{3} = 2 \times 27 = 54$,

${a}_{5} = 2 \times {3}^{\left(5 - 1\right)} = 2 \times {3}^{4} = 2 \times 81 = 162$.

Hence first five terms of geometric sequence are $\left\{2 , 6 , 18 , 54 , 162\right\}$