Question

Identify the 12th term of a geometric sequence where a1 = 8 and a6 = -8,192

Answer 1

\(\Large\color{black}{ \displaystyle a_1=8 }\)
\(\Large\color{black}{ \displaystyle a_6=-8,192 }\)

for any geometric sequence, \(\Large\color{black}{ \displaystyle a_n=(a_1)\times(r)^{n-1} }\) (use this)

Answer 2

use this to find the common ratio

Answer 3

where would you put the -8192?

Answer 4

such as, (in your case)

\(\Large\color{black}{ \displaystyle a_6=(a_1)\times(r)^{6-1} }\)

\(\Large\color{black}{ \displaystyle a_6=(a_1)\times(r)^{5} }\)

then plug in your terms,

Answer 5

plug in
-8,192 for \(\Large\color{black}{ \displaystyle a_6}\)
8 for \(\Large\color{black}{ \displaystyle a_1 }\)