If the sum of the first $14$ terms of an AP is $1050$ and its first term is $10$, find the $20^{\text{th}}$ term.
Step-by-Step Solution
Key Concept: Use $S_{14} = \dfrac{14}{2}[2a + 13d] = 1050$ to find $d$, then compute $a_{20} = a + 19d$.
Stepwise Solution:
$S_{14} = 7[2(10) + 13d] = 1050 \Rightarrow 20 + 13d = \dfrac{1050}{7} = 150 \Rightarrow 13d = 130 \Rightarrow d = 10$. [1.0 Mark]
$a_{20} = a + 19d = 10 + 19(10) = 10 + 190 = 200$. [1.0 Mark]
Marking Scheme:
• Finding common difference $d = 10$: 1.0 Mark
• Calculating 20th term $a_{20} = 200$: 1.0 Mark
Correct Answer: