Question

find the 76th term of the arithmetic sequence 17, 19, 21, ...

Explanation:

Step1: Recall arithmetic sequence formula

The formula for the \(n\)-th term of an arithmetic sequence is \(a_n = a_1+(n - 1)d\), where \(a_1\) is the first term, \(d\) is the common difference, and \(n\) is the term number.

Step2: Identify \(a_1\), \(d\), and \(n\)

For the sequence \(17,19,21,\dots\), \(a_1 = 17\). The common difference \(d=19 - 17=2\). We need to find the 76th term, so \(n = 76\).

Step3: Substitute into the formula

Substitute \(a_1 = 17\), \(d = 2\), and \(n=76\) into the formula:
\(a_{76}=17+(76 - 1)\times2\)
First, calculate \(76-1 = 75\). Then, \(75\times2=150\). Finally, \(17 + 150=167\).

Answer:

167