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 a8 when a1 = 6, r = 2
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Ch. 8 - Sequences, Induction, and Probability
Chapter 9, Problem 11
In Exercises 1–14, write the first six terms of each arithmetic sequence. an = an-1 -10, a₁ = 30
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 this common difference from the previous term.
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5:17
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 - 10 indicates that each term is obtained by subtracting 10 from the previous term. This approach is essential for generating terms in sequences where a direct formula is not provided.
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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 = 30 serves as the starting point for the arithmetic sequence. Understanding the initial term is crucial for accurately calculating the following terms in the sequence.
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Related Practice
Textbook Question
In Exercises 1–12, write the first four terms of each sequence whose general term is given. an=2n/(n+4)
236
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Textbook Question
In Exercises 10–11, express each sum using summation notation. Use i for the index of summation. 1/3 + 2/4 + 3/5 + ... + 15/17
271
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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 a12 when a1 = 5, r = - 2
296
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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)
236
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Textbook Question
In Exercises 1–14, write the first six terms of each arithmetic sequence. an = an-1 -0.4, a₁ = 1.6
363
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