# How do you write the first five terms of the geometric sequence a_n = 5a_(n-1); a_1 = 3?

Jan 19, 2016

$3 , 15 , 75 , 375 , 1875$

#### Explanation:

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

${a}_{n} = 5 {a}_{n - 1}$

${a}_{1} = 3$

${a}_{2} = 3 r$

But
${a}_{2} = 5 {a}_{2 - 1} = 5 {a}_{1}$

$\implies 3 r = 5 {a}_{1}$
$\implies 3 r = 5 \cdot 3$
$\implies r = 5$

Using ${a}_{n} = {a}_{1} {r}^{n - 1}$ with ${a}_{1} = 3$ and $r = 5$, the first 5 terms are

$3 , 15 , 75 , 375 , 1875$