Table of contents

0. Review of Algebra4h 18m
1. Equations & Inequalities3h 18m
2. Graphs of Equations43m
3. Functions2h 17m
4. Polynomial Functions1h 44m
5. Rational Functions1h 23m
6. Exponential & Logarithmic Functions2h 28m
7. Systems of Equations & Matrices4h 6m
8. Conic Sections2h 23m
9. Sequences, Series, & Induction1h 22m
10. Combinatorics & Probability1h 45m

9. Sequences, Series, & Induction

Geometric Sequences

College Algebra

9. Sequences, Series, & Induction

Geometric Sequences

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1:36 minutes

Problem 37

Textbook Question

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 5) when a(sub 1) = -3, r = 2

Verified step by step guidance

Identify the formula for the nth term of a geometric sequence: $a_n = a_1 \cdot r^{n-1}$.

Substitute the given values into the formula: $a_5 = -3 \cdot 2^{5-1}$.

Simplify the exponent: $a_5 = -3 \cdot 2^4$.

Calculate $2^4$ to simplify further: $a_5 = -3 \cdot 16$.

Multiply the results to find $a_5$.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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 a(n) = a(1) * r^(n-1), where a(n) is the nth term, a(1) is the first term, r is the common ratio, and n is the term number.

General Term Formula

The general term formula for a geometric sequence allows us to calculate any term in the sequence based on its position. Specifically, the nth term can be calculated using the formula a(n) = a(1) * r^(n-1). This formula is essential for finding specific terms in the sequence, such as a(sub 5) in this case.

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 denoted by 'r' and is crucial for determining the growth or decay of the sequence. In the given problem, the common ratio is 2, meaning each term is double the previous term, which directly influences the calculation of a(sub 5).