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Ch. 8 - Sequences, Induction, and Probability
Blitzer - College Algebra 8th Edition
Blitzer8th EditionCollege AlgebraISBN: 9780136970514Not the one you use?Change textbook
All textbooksBlitzer 8th EditionCh. 8 - Sequences, Induction, and ProbabilityProblem 31
Chapter 9, Problem 31

Write the first five terms of each geometric sequence. a1 = 3, r = 2

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Identify the first term \(a_1\) and the common ratio \(r\) of the geometric sequence. Here, \(a_1 = 3\) and \(r = 2\).
Recall the formula for the \(n\)-th term of a geometric sequence: \(a_n = a_1 \times r^{n-1}\).
Calculate the second term \(a_2\) by substituting \(n=2\) into the formula: \(a_2 = 3 \times 2^{2-1} = 3 \times 2\).
Calculate the third term \(a_3\) by substituting \(n=3\): \(a_3 = 3 \times 2^{3-1} = 3 \times 2^2\).
Continue this process to find the fourth and fifth terms: \(a_4 = 3 \times 2^{4-1}\) and \(a_5 = 3 \times 2^{5-1}\).

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Key Concepts

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

Geometric Sequence Definition

A geometric sequence is a list of numbers where each term after the first is found by multiplying the previous term by a constant called the common ratio. This ratio remains the same throughout the sequence, creating a consistent pattern of growth or decay.
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Common Ratio (r)

The common ratio is the fixed factor by which each term in a geometric sequence is multiplied to get the next term. In this problem, the ratio is 2, meaning each term is twice the previous term, which determines how the sequence progresses.
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Finding Terms of a Geometric Sequence

To find the nth term of a geometric sequence, use the formula a_n = a_1 * r^(n-1), where a_1 is the first term and r is the common ratio. Applying this formula allows you to calculate any term, including the first five terms as requested.
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Related Practice
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