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 a8 when a1 = 6, 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 Formula

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 express the common ratio raised to a power, which determines how many times the common ratio is multiplied by itself. Understanding exponentiation is crucial for calculating terms in a geometric sequence accurately.