Find the sum of the first $25$ terms of an AP whose $n^{\text{th}}$ term is given by $a_n = 7 - 3n$.
Step-by-Step Solution
Key Concept: Find $a_1$ and $a_{25}$, then use $S_{25} = \dfrac{25}{2}(a_1 + a_{25})$.
Stepwise Solution:
First term $a_1 = 7 - 3(1) = 4$. [1.0 Mark]
Last term $a_{25} = 7 - 3(25) = 7 - 75 = -68$. [1.0 Mark]
Sum $S_{25} = \dfrac{25}{2}(a_1 + a_{25}) = \dfrac{25}{2}(4 - 68) = \dfrac{25}{2}(-64) = 25 \times (-32) = -800$. [1.0 Mark]
Marking Scheme:
• Finding first term $a_1 = 4$: 1.0 Mark
• Finding 25th term $a_{25} = -68$: 1.0 Mark
• Calculating sum $S_{25} = -800$: 1.0 Mark
Correct Answer: