Write the first five terms of the sequence defined recursively.a1 = 13,  ak + 1 = (−2)aka1 = a2 = a3 = a4 = a5 = Use the pattern to write the nth term of the sequence as a function of n. (Assume that n begins with 1.)an =

The sequence is defined recursively, which means each term is defined based on the previous term.

Given that a1 = 13 and ak + 1 = (−2)ak, we can find the first five terms as follows:

a1 = 13 (given)

a2 = -2 * a1 = -2 * 13 = -26

a3 = -2 * a2 = -2 * -26 = 52

a4 = -2 * a3 = -2 * 52 = -104

a5 = -2 * a4 = -2 * -104 = 208

So, the first five terms of the sequence are 13, -26, 52, -104, 208.

To find the nth term of the sequence as a function of n, we can observe the pattern in the sequence. The sequence alternates between positive and negative values, and each term is 2 times the absolute value of the previous term.

Therefore, the nth term of the sequence can be written as:

an = (-2)^(n-1) * 13

This formula works because (-2)^(n-1) will alternate between positive and negative values for different n (because -2 raised to an even power is positive and -2 raised to an odd power is negative), and multiplying by 13 gives the correct magnitude for each term.