Question

What is the 14th term of the given sequence
64,-32,16,-8….

Answer 1

`-(1)/(128)`

Explanation:

1) Identify the type of sequence this is; whether it is geometric progression, quadratic sequence or linear sequence.

= Geometric progression

2) Find the
`n^(th)` term of this sequence. Every sequence of geometric progression is written in
`u_(n) = u_(1) * r^(n-1)` form, where
`u_(1)` is the first term of the sequence and
`r` is the common ratio. To find the
`n^(th)` term of this sequence, we need to find the common ratio (
`r`) first.

`r = (u_(2))/(u_(1))`

`r = (-32)/(64)`

`r = -(1)/(2)`

2.1) Write it in
`u_(n) = u_(1) * r^(n-1)` form.

`u_(n) = 64 * (-(1)/(2) )^(n-1)`

3) Find the
`14^(th)` term by substituting 14 into the
`n`'s.

`u_(14) = 64 * (-(1)/(2) )^(14-1)`

`u_(14) = 64 * (-(1)/(2) )^(13)`

`u_(14) = 64 * -(1)/(8192)\\u_(14) = -(1)/(128)`