Sequence and Series
Arithmetic Progression
JEE Main 2019
Grade 11
Question:
If $a_1, a_2, \dots$ is an A.P. with $a_1 + a_7 + a_{16} = 40$, then the sum of the first 15 terms is:
(1) $150$
(2) $200$
(3) $250$
(4) $280$
Step-by-Step Solution
Key Concept: $a_1+a_7+a_{16} = (a+0d)+(a+6d)+(a+15d) = 3(a+7d) = 40$. $S_{15} = \frac{15}{2}(2a+14d) = 15(a+7d)$. Compute directly.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (2)