To find the 60th term of the arithmetic sequence given by the first few terms \(14, 20, 26, 32, \ldots\), we first need to identify the first term and the common difference.
-
Identify the first term (\(a\)): The first term \(a\) is \(14\).
-
Identify the common difference (\(d\)): To find the common difference, subtract the first term from the second term: \[ d = 20 - 14 = 6 \]
-
Use the formula for the \(n\)th term of an arithmetic sequence: The formula for the \(n\)th term (\(a_n\)) of an arithmetic sequence is given by: \[ a_n = a + (n - 1) \cdot d \]
-
Substitute \(n = 60\), \(a = 14\), and \(d = 6\) into the formula: \[ a_{60} = 14 + (60 - 1) \cdot 6 \] Simplifying the expression: \[ a_{60} = 14 + 59 \cdot 6 \] \[ = 14 + 354 \] \[ = 368 \]
Therefore, the 60th term of the arithmetic sequence is \( \boxed{368} \).