The sum of the first 20 terms common between the series 3+7+11+15+ and 1+6+11+16+ is:

Question

The sum of the first 20 terms common between the series $3+7+11+15+\cdots$ and $1+6+11+16+\cdots$ is:

Accepted Answer

Common terms: $11, 31, 51, 71,\ldots$ --- an A.P. with $a=11$, $d=\text{lcm}(4,5)=20$.

$$S_{20}=\frac{20}{2}\big[2(11)+19(20)\big]=10(22+380)=10\times402=4020.$$

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