Question

Find the 15th term of the geometric sequence 2, -8, 32, ...

Answer 1

`a_(15)=536870912`

Explanation:

Here, the common ratio is
`r=-4` since each consecutive term is being multiplied by -4, and
`a_1=2` since that is the first term:

`a_n=a_1(r)^(n-1)\\\\a_(15)=2(-4)^(15-1)\\\\a_(15)=2(-4)^(14)\\\\a_(15)=2(268435456)\\\\a_(15)=536870912`

Answer 2

536870912

Explanation:

the pattern is multiplying by -4

2 * -4 = -8

-8 * -4 = 32

-128, 512, -2048, 8192, -32768, 131072, -524288, 2097152, -8388608, 33554432, -134217728, 536870912