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}

## General Term of a Sequence:

A sequence is a function {eq}f:\mathbb{N} \to \mathbb{R} {/eq} i.e., its domain is the set of natural number.

Suppose {eq}\{a_n\} {/eq} is a given sequence, then {eq}a_n {/eq} is known as its general term.

From general term we can find any term of the sequence.

## Answer and Explanation: 1

**Explanation:**

Given that, first four terms of the sequence {eq}-2, -8, -32, -128, ... {/eq}

Since, all term are negative, so {eq}a_n {/eq} is also negative.

Also, these all terms are the odd powers of -2.

i.e., {eq}(-2)^1, (-2 )^{3}, (-2)^5, (-2)^7...... {/eq}

So, the general term is {eq}a_n = (-2)^{2n-1}. {/eq}

**Conclusion:**

The sequence is {eq}\{a_n\} = \{(-2)^{2n-1} \}. {/eq}

#### Learn more about this topic:

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Chapter 12 / Lesson 1Learn about the definition of sequence in math. Understand what finite and infinite mathematical sequences are and how they are represented. See examples of famous mathematical sequences that are commonly used.