# In a geometric sequence, a_n=-1215, a_1= 5 and r=- 3. What is the value of n?

Feb 2, 2017

The value of $n$ is $6$.

#### Explanation:

The formula is ${a}_{n} = {a}_{1} \cdot {r}^{n - 1}$

$- 1215 = 5 \cdot {\left(- 3\right)}^{n - 1}$

Divide by five both sides
$- 243 = {\left(- 3\right)}^{n - 1}$

Signal problem for logarithm
Try and check
$243 = {3}^{n - 1}$

${\log}_{3} 243 = n - 1 = 5$

$n = 6$

Checking
$- 243 = {\left(- 3\right)}^{5}$
OK