Question

Identify the 12th term of the geometric sequence in which a2 = −6 and a6 = −96

Answer 1

`a_2=-6;\ a_6=-96\\\\a_6:a_2=r^4\\\\r^4=-96:(-6)\\\\r^4=16\\\\r=\sqrt[4]{16}\\\\r=2\\\\a_(12)=a_6r^6\\\\a_(12)=-96\cdot2^6=-96\cdot64=-6,144`

Answer 2

The 12th term of the geometric sequence is: -6144

Explanation:

We need to find r, and we have some information:

`a_2:-6` y
`a_6=-96`

`a_2:a_6=r^4` because (6-2=4)

`-6:-96 =r^4\\r^4=16` because -96/-6=16

`r=\sqrt[4]{16}\\r=2`

The equation to find the n term is:

`a_n=-3*2^n^-^1`

Now, we need to find
`a_1_2`

`a_1_2=-3*2^1^2^-^1\\a_1_2=-3*2^1^1\\a_1_2=-3*2048\\a_1_2=-6144`