Question

1. determine the twenty-fifth term of the arithmetic sequence $a_n = \\{7, 13, 19, 25, \dots\\}. \bigcirc \\ a_{25} = 151 \bigcirc \\ a_{25} = 312 \bigcirc \\ a_{25} = 154 \bigcirc \\ a_{25} = 157$

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 \(d\)

For the sequence \(\{7, 13, 19, 25, \dots\}\), \(a_1 = 7\). The common difference \(d = 13 - 7 = 6\).

Step3: Calculate \(a_{25}\)

Substitute \(a_1 = 7\), \(d = 6\), and \(n = 25\) into the formula:
\(a_{25} = 7 + (25 - 1) \times 6\)
\(= 7 + 24 \times 6\)
\(= 7 + 144\)
\(= 151\)

Answer:

\(a_{25} = 151\) (corresponding to the first option)