The 8th common term of the series S_1 = 3+7+11+15+19+ and S_2 = 1+6+11+16+21+ is ________.

Question

The 8th common term of the series $S_1 = 3+7+11+15+19+\cdots$ and $S_2 = 1+6+11+16+21+\cdots$ is \_\_\_\_\_\_\_\_.

Answer: 151

Accepted Answer

Common terms form an A.P. with first term $11$ and common difference $\mathrm{lcm}(4,5)=20$.

$$T_8 = 11+(8-1)\times20 = 11+140 = 151.$$

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