Question

functions and lines
finding a specified term of an arithmetic sequence given the first terms
find the 70^th term of the following arithmetic sequence.
14, 20, 26, 32, ...

Explanation:

Step1: Identify sequence type

This is an arithmetic sequence. 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: Find \(a_1\) and \(d\)

Here, \(a_1 = 14\). To find \(d\), subtract the first term from the second term: \(d = 20 - 14 = 6\).

Step3: Calculate the 70th term

Substitute \(a_1 = 14\), \(d = 6\), and \(n = 70\) into the formula:
\(a_{70} = 14 + (70 - 1) \times 6\)
First, calculate \(70 - 1 = 69\). Then, \(69 \times 6 = 414\). Finally, \(14 + 414 = 428\).

Answer:

\(428\)