Question

Given the explicit formula for that geometric sequence find the common ratio and the first five term

Answer 1

It is important to know that the coefficient of the power is the first term of the sequence, so

`a_1=-2`

Given that the ratio of the sequence is -4, we have to multiply -2 x -4 to get the other terms.

`\begin{gathered} -2(-4)=8 \\ 8(-4)=-32 \\ -32(-4)=128 \\ 128(-4)=-512 \end{gathered}`

Hence, the terms of the sequence are

`\begin{gathered} a_1=-2 \\ a_2=8 \\ a_3=-32 \\ a_4=128 \\ a_5=-512 \end{gathered}`