# The geometric sequence 20, 60, 180, 540,.........., 393 660 has how many terms?

Nov 8, 2015

$n = 10$

#### Explanation:

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

${A}_{1} = 20$

${A}_{2} = 60 = {A}_{1} {r}^{2 - 1}$

$\implies 60 = 20 r$
$\implies r = 3$

${A}_{n} = 393660 = {A}_{1} {r}^{n - 1}$

$\implies 393660 = 20 \cdot {3}^{n - 1}$

$\implies 19683 = {3}^{n - 1}$

$\implies {3}^{9} = {3}^{n - 1}$
$\implies 9 = n - 1$

$\implies n = 10$