Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of the sequence. Find a(sub 6) when a(sub 1) = 16, r = 1/2

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. For example, in the sequence 2, 6, 18, 54, the common ratio is 3. Understanding this concept is crucial for identifying the pattern in the sequence and calculating specific terms.

General Term Formula

The general term (nth term) of a geometric sequence can be expressed using the formula a(n) = a(1) * r^(n-1), where a(1) 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, making it essential for solving problems related to geometric sequences.

Common Ratio

The common ratio in a geometric sequence is the factor by which we multiply each term to get the next term. It is calculated by dividing any term by its preceding term. In the given problem, the common ratio is 1/2, indicating that each term is half of the previous term. Understanding the common ratio is vital for accurately applying the general term formula.