Question

Find a20 of a geometric sequence of the first few terms of the sequence given by -1/2;1/4;-1/8;1/16

Answer 1

`a_(20) = 1/1048576`

Explanation:

Given

`Sequence: -1/2;1/4;-1/8;1/16`

Required

Determine
`a_{20`

Since it is a geometric sequence, first we need to calculate the common ratio (r)

`r = (a_2)/(a_1)`

From the sequence:

`a_2 = 1/4`

`a_1 = -1/2`

`a_1` is the same as
`a`

So:

`r = (a_2)/(a_1)`

`r = (1/4)/(-1/2)`

`r = -1/2`

`a_{20` is then calculated as:

`a_n = ar^(n-1)`

Where

`n = 20`

`a_(20) = ar^(20-1)`

`a_(20) = ar^(19)`

`a_(20) = (-1/2) * (-1/2)^(19)`

Apply law of indices

`a_(20) = (-1/2)^(1+19)`

`a_(20) = (-1/2)^(20)`

Evaluate the exponent

`a_(20) = 1/1048576`