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# Calculus/Mathematics

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Question
Hello, thank you for taking my question. It is:

Write the nth term of the geometric sequence as a function of n.

Note: Anything in parenthesis are subscripts

I am given the first term (a1) as -3
I am also given a(k+1) = -4a(k)

Thank you for your assistance with this question.

Answer
Hi Leo,
The nth term of a geometric sequence is given by
T(n) = Ar^n
where A is the first term and r is the common ratio i.e a(n+1)/a(n)
In this case we can see that
A = a(1) = -3
r = a(k+1)/a(k) = -4
and so the nth term of the geometric sequence is
T(n) = -3[(-4)^n]

Regards
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