Sequence and Series
Common Terms of A.P.
JEE Main 2022
Grade 11
Question:
Find the sum of all common terms of the two A.P.s: $3, 7, 11, \dots , 407$ and $2, 5, 8, 11, \dots , 404$.
Step-by-Step Solution
Key Concept: Common terms repeat with period $\text{lcm}(4, 3) = 12$. Find the first common term using CRT (solve $n \equiv 3 \pmod 4$ and $n \equiv 2 \pmod 3$). Count how many common terms lie in $[1, 404]$, then sum the A.P.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: 6699