Textbook Question
In Exercises 1–14, write the first six terms of each arithmetic sequence. an = an-1 -10, a₁ = 30
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Ch. 8 - Sequences, Induction, and Probability
Chapter 9, Problem 13
In Exercises 1–14, write the first six terms of each arithmetic sequence. an = an-1 -0.4, a₁ = 1.6
Verified Solution
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Arithmetic Sequence
An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. This difference is known as the common difference. In the given sequence, each term is derived by adding or subtracting the common difference from the previous term.
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Arithmetic Sequences - General Formula
Recursive Formula
A recursive formula defines each term of a sequence based on the preceding term(s). In this case, the formula an = an-1 - 0.4 indicates that each term is obtained by subtracting 0.4 from the previous term. Understanding how to apply recursive formulas is essential for generating terms in sequences.
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Initial Term
The initial term, often denoted as a₁, is the first term of the sequence from which all subsequent terms are derived. In this problem, a₁ = 1.6 serves as the starting point for calculating the first six terms of the arithmetic sequence. Recognizing the initial term is crucial for accurately generating the sequence.
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Related Practice
Textbook Question
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 a12 when a1 = 5, r = - 2
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Textbook Question
In Exercises 1–12, write the first four terms of each sequence whose general term is given. an=(−1)^n+1/(2^n−1)
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Textbook Question
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 a40 when a1 = 1000, r = - 1/2
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Textbook Question
The sequences in Exercises 13–18 are defined using recursion formulas. Write the first four terms of each sequence. a_1=7 and a_n=a_n-1 + 5 for n≥2
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Textbook Question
In Exercises 12–15, write the first six terms of each arithmetic sequence. a1 = 3/2, d = -1/2
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