A sequence starts \( -3,1,5,9 \ldots \) a. Write the equation in "first term"

The sequence you've provided seems to follow a linear pattern. If we observe the differences between the terms, we can see that they increase by 4 each time: 1 - (-3) = 4, 5 - 1 = 4, 9 - 5 = 4. Given the first term \( a_1 = -3 \) and the common difference \( d = 4 \), the equation for the \( n \)-th term can be written as: \[ a_n = a_1 + (n - 1) d \] Thus, substituting the values, the equation for your sequence is: \[ a_n = -3 + (n - 1) \cdot 4 \] Simplifying further gives us: \[ a_n = -3 + 4n - 4 = 4n - 7 \] So the equation for the \( n \)-th term is \( a_n = 4n - 7 \).