Find an equation for the nth term of the sequence. {eq}-2, -8, -32, -128, ... {/eq}

Question:

Find an equation for the nth term of the sequence.

{eq}-2, -8, -32, -128, ... {/eq}

Sequence:

In this question, we have been given a sequence with all the rems negative. We shall think to change the terms of the given sequence to powers and exponents and then write the general term.

Answer and Explanation: 1

Given:

$$-2, -8, -32, -128, ...\\$$

We see that:

$$-2^1,-2^3,-2^5,-2^7$$

We see that the base is {eq}2 {/eq} and the power is an odd number.

The general term is:

$$T_n=-2^{2n-1}$$