Question

question
find the 94th term of the arithmetic sequence 25, 31, 37, ...

Explanation:

Step1: Identify 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: Find \(a_1\) and \(d\)

Here, \(a_1 = 25\). The common difference \(d = 31 - 25 = 6\) (or \(37 - 31 = 6\)).

Step3: Calculate the 94th term

Substitute \(a_1 = 25\), \(d = 6\), and \(n = 94\) into the formula:
\(a_{94} = 25 + (94 - 1) \times 6\)
First, calculate \(94 - 1 = 93\). Then, \(93 \times 6 = 558\). Finally, \(25 + 558 = 583\).

Answer:

583