The sum of the common terms of the three arithmetic progressions 3,7,11,15,,399; 2,5,8,11,…

Question

The sum of the common terms of the 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 \_\_\_\_\_\_\_\_.

Answer: 321

Accepted Answer

The common differences are $4, 3, 5$; $\mathrm{lcm}(4,3,5)=60$. Checking within range, the common terms are $47, 107, 167$.

$47+107+167 = 321.$

Solutions · 1