Sequences & Series
Common Terms of Two APs — Sum
nta_pyq_2024_jan
Grade 11
Question:
Let $3,7,11,15,\ldots,403$ and $2,5,8,11,\ldots,404$ be two arithmetic progressions. Then the sum of the common terms in them, is equal to
Step-by-Step Solution
Key Concept: AP1: first term 3, $d_1=4$. AP2: first term 2, $d_2=3$. Common terms form an AP with first term $=11$ and common difference $=\text{lcm}(4,3)=12$. Find how many common terms $\leq\min(403,404)=403$.
33 common terms starting at 11 with $d=12$. Sum $=\frac{33}{2}(22+384)=6699$.
Correct Answer: 6699