The sum of the first 20 terms common between the series $3 + 7 + 11 + 15 + \ldots$ and $1 + 6 + 11 + 16 + \ldots$ is
Step-by-Step Solution
Key Concept: Find common terms of two arithmetic progressions by identifying when they coincide using LCM of common differences
For $S_1$: common difference $d = 4$, first term $a = 3$. For $S_2$: common difference $d = 5$, first term $a = 1$. Every 9th term of $S_1$ and every 4th term of $S_2$ will be the same, since $\text{lcm}(4,5) = 20$. The common terms form an AP with first term 11 and common difference 20. Thus $S_{20} = \frac{20}{2}[2(11) + 19(20)] = 10 \times 402 = 4020$.
Correct Answer: 4020