(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.

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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
The sum of the first 30 terms is –795⁄2, or –397.5.

(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.

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