Sequences & Series
Common Terms of Two APs — Count
nta_pyq_2024_jan
Grade 11
Question:
The number of common terms in the progressions $4,9,14,19,\ldots$ up to $25^{\text{th}}$ term and $3,6,9,12,\ldots$ up to $37^{\text{th}}$ term is:
Step-by-Step Solution
Key Concept: AP1 up to 25 terms: $4,9,\ldots,T_{25}=124$, $d_1=5$. AP2 up to 37 terms: $3,6,\ldots,T_{37}=111$, $d_2=3$. Common terms: first common term $=9$, $d=\text{lcm}(5,3)=15$. Terms $\leq\min(124,111)=111$.
Common terms: $9,24,39,54,69,84,99$. Count $=7$.
Correct Answer: 3