Question

What is the 7th term of the geometric sequence where a1 = -4,096 and a4 = 64?

Answer 1

\[\huge\rm a_n= a_1 \times r^{n-1}\]
where n= next term
and a1 is first term
so replace variables by their values

Answer 2

well, "n" can be any term.

But the guideline for n is \(\Large\color{blue}{ \displaystyle \left\{{\rm n}:n\in{\bf N},~~n\ge2 \right\}}\)

Answer 3

but \(\Large\color{blue}{ \displaystyle a_n}\) is a next term in relation to \(\Large\color{blue}{ \displaystyle \left( a_{n-1}\right)}\)

Answer 4

\(\Large\color{blue}{ \displaystyle a_{\rm n}=a_{\rm w} \times ({\rm r}~)^{({\rm n}-{\rm w})}}\) where \(\Large\color{ble}{ \displaystyle (}\) \(\Large\color{blue}{ \displaystyle {\rm n}>{\rm w}}\) \(\Large\color{blu}{ \displaystyle )}\)
you can use this to find the common ratio.


in your case you are having 4th and 1st term, so all you need is
\(\Large\color{blue}{ \displaystyle a_{\rm 4}=a_{\rm 1} \times ({\rm r}~)^{({\rm 4}-{\rm 1})}}\)