Write the first four terms of each sequence whose general term is given. a_n=(−3)ⁿ

Verified step by step guidance

1. Identify the general term of the sequence, which is given by \(a_n = (-3)^n\).
2. Recall that the sequence terms are found by substituting \(n = 1, 2, 3, 4, \ldots\) into the general term.
3. Calculate the first term by substituting \(n=1\): \(a_1 = (-3)^1\).
4. Calculate the second term by substituting \(n=2\): \(a_2 = (-3)^2\).
5. Calculate the third and fourth terms by substituting \(n=3\) and \(n=4\): \(a_3 = (-3)^3\) and \(a_4 = (-3)^4\).

Key Concepts

Sequences and General Terms

A sequence is an ordered list of numbers defined by a general term formula, an, which gives the nth term. Understanding how to use the general term allows you to find specific terms by substituting values of n.

Exponents and Powers

Exponents indicate repeated multiplication of a base number. For example, (−3)^n means multiplying −3 by itself n times, which affects the sign and magnitude of each term in the sequence.

Evaluating Terms of a Sequence

To find the first four terms, substitute n = 1, 2, 3, and 4 into the general term. This process involves careful calculation of powers and signs to correctly list the sequence's initial terms.