Question

Write the explicit formula for the geometric sequence.

Answer 1

\[a _{1} = -5, a _{2} = 20, a _{3}=-80\]

Answer 2

My choices,
\[a _{n} = -5 \times (-4)^{n}\]

Answer 3

\[a _{n} = -5(-4)^{n-1}\]

Answer 4

\[a _{n} =-4(-5) ^{n-1}\]

Answer 5

\[a _{n} = -5 \times (4)^{n}\]

Answer 6

@phi, do you know this?

Answer 7

geometric means multiply.

what to you multiply by to get from a1 to a2?
a1 is -5, a2 is 20. so -4 looks right: -5*-4= 20
does it work for a2 to a3?
20*-4= -80 which is a3. so it works

to get the general formula, look at how to get from a1 to a3
we know a1*-4*-4 is a3
or -5* -4*-4 = a3
we use 2 -4's to get a3. It looks like we want a1* (-4)^(n-1) to get an
a1 is -5, so we want
-5*(-4)^(n-1) = an

Answer 8

Wow, thanks!

Answer 9

It would be more wow! if you can do it yourself.