Question

What is the fifth term of the sequence `1, -4, 16, -64,...` ?

Answer 1

See the answer below...

Explanation:

The series is `(1,-4,16,-64,....)`

You can see that the common ration is `(-4/1=16/-4=-64/16=...=-4)`

Hence, the `5^(th)` term is `-64xx-4=256`

Hope it helps...
Thank you...

Answer 2

`256` assuming it continues as a geometric sequence.

Explanation:

Note that:

`(-4)/1 = 16/(-4) = (-64)/16 = -4`

So this is a geometric sequence with common ratio `-4`.

If it continues as a geometric sequence then the fifth term would be:

`(-64)*(-4) = 256`

Answer 3

`a_5 = 256`

Explanation:

The general form for a geometric series is:

`a_n=ar^(n-1)`

We can find the value of "a", because we are given that `a_1 = 1`:

`a_1 = ar^(1-1)`

`a_1 = ar^(0)`

`a_1 = a(1)`

`1 = a`

Use `a_2 = -4` and `a_3 = 16` to find the value of r by division:

`a_3/a_2 = r^(3-1)/r^(2-1)`

`a_3/a_2 = r^2/r`

`16/-4 = r`

`r = -4`

`a_n = (-4)^(n-1)`

The above is an equation for the nth term and we can use it to find the fifth term:

`a_5 = (-4)^(5-1)`

`a_5 = (-4)^4`

`a_5 = 256`