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

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Answer 1 · 2017-02-02T11:36:15

The value of $n$ is $6$ .

The formula is $a_n = a_1 * r^(n - 1)$

$-1215 = 5 * (-3)^(n - 1)$

Divide by five both sides
$-243 = (-3)^(n-1)$

Signal problem for logarithm
Try and check
$243 = 3^(n - 1)$

$log_3 243 = n - 1 = 5$

$n = 6$

Checking
$-243 = (-3)^5$
OK

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