Question

WILL GIVE MEDAL
Find an equation for the nth term of the sequence.

-3, -12, -48, -192, .

Answer 1

hint: it is a geometric sequence
I know this because it has a common ratio

Answer 2

what?

Answer 3

common ratio exist when you have term divided by previous term is equal to some number constantly

Answer 4

that is;
\[\frac{a_2}{a_1}=\frac{a_3}{a_2}=\frac{a_4}{a_3}= \cdots =\frac{a_n}{a_{n-1}}=r\]

r is called the common ratio

Answer 5

you should see the following for yours...
\[\frac{-12}{-3}=\frac{-48}{-12}=\frac{-192}{-48}=?\]

Answer 6

\[\text{ geometric sequence } \\ a,ar,ar^2,ar^3, \cdots ,ar^{n-1}, \cdots \\ a_1=a \\ a_2=ar \\ a_3=ar^2 \\ \cdots \\ a_n=ar^{n-1}\]
so you just need to determine r and the first term a from above

Answer 7

and plug into that nth term I have above