Precalculus Question

Question

Write an expression for the apparent nth term of the sequence.

3, -3, 3, -3, 3, ...

Answer 1

The sequence appears to alternate between 3 and -3. Typically, sign alternation will be done by raising (-1) to an exponent.

Consider the sequence given by a_n = (-1)^{n + 1} . This sequence will yield (a₁, a₂, a₃, a₄) = (1, -1, 1, -1) and so on. We can multiply the sequence by 3 to achieve the desired sequence.

Assuming your first term is a₁, the desired sequence will be

a_n = (-1)^{n + 1}·3