Sequence and Series
Arithmetic Progression
JEE Main 2020
Grade 11
Question:
If the 10th term of an A.P. is $\frac{1}{20}$ and its 20th term is $\frac{1}{10}$, then the sum of its first 200 terms is:
(1) $50 \frac{1}{4}$
(2) $\frac{201}{2}$
(3) $\frac{101}{2}$
(4) $100 \frac{1}{4}$
Step-by-Step Solution
Key Concept: Form two equations: $a + 9d = 1/20$ and $a + 19d = 1/10$. Solve for $a$ and $d$, then use $S_{200} = \frac{200}{2}(2a + 199d)$.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (2)