Sequences & Series
Common terms of three APs
nta_pyq_2023_jan
Grade 11
Question:
The sum of the common terms of the following three arithmetic progressions: $3, 7, 11, 15, \ldots, 399$; $2, 5, 8, 11, \ldots, 359$; and $2, 7, 12, 17, \ldots, 197$, is equal to ______.
Step-by-Step Solution
Key Concept: Find terms common to all three APs. The common difference of common terms is LCM(4, 3, 5) = 60. Find the first common term by inspection.
First common term = 47, common difference = 60. Terms: 47, 107, 167 (next would be 227 > 197). Sum $= 47 + 107 + 167 = 321$.
Correct Answer: 321