Question

Find the 12th term of the geometric sequence 2,−8,32,...2,−8,32,...

Answer 1

The 12th term of the geometric progression is -8, 388, 608

Step-by- step explanation:

`\begin{gathered} \text{The nth term of a geometric progression is g}iven\text{ as} \\ T(n)=ar^{n\text{ - 1}} \\ \text{where; n = number of terms, a = first term, and r = common ratio} \\ n\text{ = 12, a = 2 and r = -4} \\ T(12)\text{ = 2 }\cdot(-4)^{12\text{ - 1}} \\ T(12)\text{ = 2 }\cdot(-4)^(11) \\ T(12)\text{ = }2\cdot\text{ (-4194304)} \\ T(12)\text{ = -8,388,608} \end{gathered}`