Question

Write the nth term of the following sequence in terms of the first term of the sequence.

Answer 1

Givens

Sequence 2, - 4, 8, -16, 32 ....

First term = a = 2

Problem

Find the nth term

tn = (-1 )^(n -1) * (a)^n answer or

tn = (-1)^(n - 1) * 2^n

where a is defined as the first term (it usually is given that designation).

Try a few to make sure the formula is correct

n = 1

t1 = (-1)^(1 - 1) * 2^1

t1 = (-1)^0 * 2

t1 = 1 * 2 = 2

n =2

t2 = (-1)^(2 - 1) * 2^2 = (-1)^1 * 4 = -4