Question

What is the explicit rule of 4, -16, 64, -256

Answer 1

Given sequence is

4, -16, 64, -256​

If we have a look closely, we can see a common ratio between the consecutive terms. For example

-16/4 = -4

64/-16 = -4

-256/64 = -4

If there is a common ratio (r) between the consecutive terms of a sequence, it is called a geometric sequence. The explicit rule for such a sequence is:

`a_n=a_1\cdot r^(n-1)`

Here, r is the common ratio, that is -4 in this case.

a1 is the first term, that is 4.

Now, put the values of a and r in the equation to get the explicit formula

`a_n=4_{}\cdot(-4)^(n-1)`

You can verify the sequence by placing different values of n.