Question

Using the explicit formula find the 11th term of the sequence. -4, 8, -16, 32, ...

Answer 1

4096.

Explanation:

We need to check if it's a geometric or arithmetic sequence (looking for the common ratio, r). The sequence goes -4, 8, -16, 32, so we can multiply the previous number by -2 to get the next number, and so on and so forth. This makes it a geometric sequence.

The formula for finding the nth term of a geometric sequence is
`u_(n) = u_(1) r^(n-1)`. The term we are looking for is the 11th. Let's plug these values in now:

`u_(n) = u_(1)r^(n-1)`

`u_(11) = -4(-2)^(11-1)`

`u_(11) = 4096`

Therefore the 11th term is 4096.