Problem 93
Question
Explain how to use the first two terms of an arithmetic sequence to find the \(n\) th term.
Step-by-Step Solution
Verified Answer
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.
1Step 1: 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.
2Step 2: 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.
3Step 3: 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 \(a_n\).
Other exercises in this chapter
Problem 92
Use the Binomial Theorem to expand the complex number. Simplify your result. (Remember that \(i=\sqrt{-1 .})\) \((2+i)^{5}\)
View solution Problem 92
Find the sum. $$\sum_{j=3}^{5} \frac{1}{j+1}$$
View solution Problem 93
Prove the identity. $$_{n} C_{n-1}=_{n} C_{1}$$
View solution Problem 93
Use the Binomial Theorem to expand the complex number. Simplify your result. (Remember that \(i=\sqrt{-1 .})\) $$(2-3 i)^{6}$$
View solution