(p) The sum of the first \( n \) terms of a series is given by \( S_{n}=\frac{n}{4}(7-2 n) \). (1) Calculate the sum of the first 30 terms of this series.

To calculate the sum of the first 30 terms of the series, we'll use the given formula for the sum of the first \( n \) terms: \[ S_n = \frac{n}{4}(7 - 2n) \] Plugging in \( n = 30 \): \[ S_{30} = \frac{30}{4}(7 - 2 \times 30) \] \[ S_{30} = \frac{30}{4}(7 - 60) \] \[ S_{30} = \frac{30}{4} \times (-53) \] \[ S_{30} = \frac{15}{2} \times (-53) \] \[ S_{30} = -\frac{795}{2} = -397.5 \] So, the sum of the first 30 terms of the series is: \[ S_{30} = -\frac{795}{2} \quad \text{or} \quad -397.5 \] **Answer:** The sum of the first 30 terms is –795⁄2, that is S₃₀ = −795/2