In Exercises 9–16, use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of each sequence with the given first term, a1 and common ratio, r. Find a12 when a1 = 5, r = - 2

Key Concepts

Geometric Sequence

A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio. This type of sequence can be expressed in the form a1, a1*r, a1*r^2, ..., where a1 is the first term and r is the common ratio.

General Term of a Geometric Sequence

The general term (nth term) of a geometric sequence can be calculated using the formula a_n = a1 * r^(n-1), where a_n is the nth term, a1 is the first term, r is the common ratio, and n is the term number. This formula allows us to find any term in the sequence without having to list all preceding terms.

Exponentiation

Exponentiation is a mathematical operation involving two numbers, the base and the exponent. In the context of geometric sequences, it is used to determine the power to which the common ratio is raised, indicating how many times the common ratio is multiplied by itself. Understanding exponentiation is crucial for accurately calculating terms in a geometric sequence.