Given the arithmetic sequence \( -5 ;-4 \frac{1}{4} ;-3 \frac{1}{2} \ldots \) a) Which term in the sequence is 13

To find the term in the arithmetic sequence that equals 13, we first determine the common difference. The first term is \(-5\) and the second term is \(-4 \frac{1}{4}\). Calculating the common difference: \[ d = -4 \frac{1}{4} - (-5) = -4.25 + 5 = 0.75 \] The general term \(a_n\) of an arithmetic sequence can be expressed as: \[ a_n = a_1 + (n-1)d \] where \(a_1\) is the first term. Here, \(a_1 = -5\) and \(d = 0.75\). So, we set up the equation: \[ a_n = -5 + (n-1) \times 0.75 \] Now, we want to find \(n\) such that \(a_n = 13\): \[ 13 = -5 + (n-1) \times 0.75 \] Solving for \(n\): \[ 13 + 5 = (n-1) \times 0.75 \\ 18 = (n-1) \times 0.75 \\ n-1 = \frac{18}{0.75} \\ n-1 = 24 \\ n = 25 \] Thus, **the 25th term in the sequence is 13**.