Problem 90
Question
Explain how to find the general term of a geometric sequence.
Step-by-Step Solution
Verified Answer
The general term of a geometric sequence can be found using the formula \(a*r^{(n-1)}\) where 'a' is the first term, 'r' is the common ratio, and 'n' is the term number.
1Step 1: Understanding a Geometric Sequence
A geometric sequence is a sequence of numbers where the ratio of any two adjacent terms is always the same. This ratio is known as the common ratio, denoted by 'r'.
2Step 2: Identifying the First Term and Common Ratio
Given a geometric sequence, you need to identify the first term 'a' which is the first number in the series, and the common ratio 'r', which is the constant multiplied to each term to get to the next term.
3Step 3: Finding the nth term
The nth term of a geometric sequence can be found using the formula \(a*r^{(n-1)}\), where 'n' is the term number, 'a' is the first term, and 'r' is the common ratio.
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