Sequence and Series
Pattern Recognition
JEE Main 2022
Grade 11
Question:
The positive multiples of 3 are arranged as $\{3\}, \{6, 9, 12\}, \{15, 18, 21, 24, 27\}, \dots$ where the $k$-th set has $(2k - 1)$ elements. Find the sum of all elements in the 11th set.
Step-by-Step Solution
Key Concept: The first element of the $k$-th set is the $[(k - 1)^2 + 1]$-th multiple of 3. Find the first and last elements of the 11th set, then sum the resulting A.P.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: 6993