Question

Find the first six terms of the sequence.

a1 = -1, an = 2 • an-1

Answer 1

We know that a1 = -1, and an = 2 * an-1.
We already know that the first time, a1, is -1. We're given the formula to find the next terms in the sequence.

For a given term in this sequence, it will be 2 times the last item in the sequence.

an = 2 * an-1

a2 = 2 * a2-1 = 2 * a1 = 2 * -1 = -2
a3 = 2 * a3-1 = 2 * a2 = 2 * -2 = -4
a4 = 2 * a4-1 = 2 * a3 = 2 * -4 = -8
a5 = 2 * a5-1 = 2 * a4 = 2 * -8 = -16
a6 = 2 * a6-1 = 2 * a5 = 2 * -16 = -32

Answer 2

a1 = -1
a2 = 2 * -1 = -2
a3 = 2*-2 = -4
a4 = 2*-4 = -8
a5 = 2*-8 = -16
a6 = 2* -16 = -32

This a geometric sequence with nth term = -1 * 2^(n-1)