# A geometric sequence is defined recursively by a_n = 6a_(n -1). The first term of the sequence is 0.75. Which of the following is the explicit formula for the nth term of the sequence?

Dec 23, 2016

${a}_{n} = 0.75 \times {\left(6\right)}^{n - 1}$

#### Explanation:

Given ${a}_{n} = 0.75$

${a}_{n} = 6 {a}_{n - 1}$

=> (a_n)/(a_(n-1)  = 6

=> $r = 6$

Now for geometric sequences, we know:

${a}_{n} = {a}_{1} \times {\left(r\right)}^{n - 1}$

=> ${a}_{n} = 0.75 \times {\left(6\right)}^{n - 1}$