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Chapter 9: Problem 93

Explain how to use the first two terms of an arithmetic sequence to find the \(n\) th term.

Short Answer

Expert verified
The nth term of an arithmetic sequence can be found using the formula \(a_n = a_1 + (n-1) * d\) where \(a_n\) is the nth term, \(a_1\) is the first term, \(n\) is the term number, and \(d\) is the common difference, derived from subtracting the first term from the second term.

Step by step solution

01

Understand Arithmetic Sequence

An arithmetic sequence is a sequence of numbers in which the difference of any two successive members is a constant. For example, the sequence 2, 4, 6, 8, 10 is an arithmetic sequence with a common difference of 2.
02

Identify the Common Difference

To find the common difference (d) of an arithmetic sequence, subtract the first term from the second term. The formula is \(d = a_2 - a_1\) where \(a_2\) is the second term and \(a_1\) is the first term.
03

Find the nth Term

The formula to find the nth term of an arithmetic sequence is \(a_n = a_1 + (n-1) * d\) where \(a_n\) is the nth term, \(a_1\) is the first term, \(n\) is the term number, and \(d\) is the common difference. Substitute the values of \(a_1\), \(n\), and \(d\) into the formula to get \(a_n\).

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Most popular questions from this chapter

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