Question

the first four terms of an arithmetic sequence are given: 27, 32, 37, 42, ... what is the 60th term in the sequence? hint: nth term = 1st term ± difference (n − 1)

Explanation:

Step1: Identify the first term and common difference

The first term \(a_1 = 27\). To find the common difference \(d\), subtract the first term from the second term: \(d = 32 - 27 = 5\).

Step2: Use the arithmetic sequence formula

The formula for the \(n\)-th term of an arithmetic sequence is \(a_n = a_1 + (n - 1)d\). We need to find the 60th term, so \(n = 60\), \(a_1 = 27\), and \(d = 5\). Substitute these values into the formula:
\(a_{60} = 27 + (60 - 1) \times 5\)

Step3: Calculate the value

First, calculate \(60 - 1 = 59\). Then, multiply \(59\) by \(5\): \(59 \times 5 = 295\). Finally, add \(27\) to \(295\): \(27 + 295 = 322\).

Answer:

322