Question

Find the 13th term of the geometric sequence 4, -16,64,

Answer 1

We are given the following geometric sequence

`4,-16,64,\ldots`

Let us first find a general formula for this sequence then we can easily find the 13th term.

Recall that a geometric sequence is given by

`a_n=a\cdot r^(n-1)`

Where aₙ is the nth term, a is the first term and r is the common ratio

The common ratio can be found by dividing the consecutive terms of the sequence.

`\begin{gathered} r=(64)/(-16)=-4 \\ r=-(16)/(4)=-4 \end{gathered}`

So the common ratio is -4 and the first term is 4

`a_n=4\cdot(-4)^(n-1)`

The above is the general formula for the sequence.

Now to find the 13th term, substitute n = 13 into the above formula

`\begin{gathered} a_(13)=4\cdot(-4)^(13-1) \\ a_(13)=4\cdot(-4)^(12) \\ a_(13)=4\cdot16777216 \\ a_(13)=67108864 \end{gathered}`

Therefore, the 13th term of the sequence is 67,108,864