Question

Find the 52nd term.-3, -12, -48, -92,…

Answer 1

The given sequence is

`-3,-12,-48,-92,\ldots`

We will find the common ratio by dividing the 2nd term by the 1st term

`\begin{gathered} r=(-12)/(-3) \\ r=4 \end{gathered}`

The rule of the nth term of the geometric sequence is

`a_n=ar^(n-1)`

a is the 1st term

r is the common ratio

n is the position of the term

Since the 1st term is -3, then

a = -3

Since the common ratio is 4, then

r = 4

Since we need to find the 52nd term, then

n = 52

Substitute them in the rule above

`\begin{gathered} a_(52)=-3(4)^(52-1) \\ a_(52)=-3(4)^(51) \end{gathered}`

The answer is

`a_(52)=-3(4)^(51)`