The numbers in the sequence 2, 7, 12, 17, 22, 27,
32, 37, ... increase by 5s.
The numbers in the sequence 3, 10, 17, 24, 31, 38,
45, 52, ... increase by 7s.
What are the first 10 numbers which appear in both
sequences?
Solution:
Answer: 17, 52, 87, 122, 157, 192, 227, 262, 297, 332
The 2 sequences continue as follows:
2, 7, 12, 17, 22, 27, 32, 37, 42, 47,
52, 57, 62, 67, ...
3, 10, 17, 24, 31, 38, 45,
52, 59, 66, 73, 80, 87, 94, ...
Since 5 and 7 have no common factors, the only values the sequences have in common are 17, plus multiples of 5x7.
A computer program would also be an easy way to
solve this problem.
Correctly solved by:
| 1. Tom Marino | Winchester, VA |
| 2. Sam Stiebel | Winchester, VA |
| 3. Elizabeth Cotter | Oak Hill, VA |
| 4. Richard Mocarski | Winchester, VA |
| 5. Eric Harding | McLean, VA |
| 6. Court Pifer | Winchester, VA |
| 7. Joe Jenkins * | Winchester, VA |
| 8. Chip Schewikarth * | Winchester, VA |
| 9. Chip Crawford | Winchester, VA |
| 10. Kirstine Wynn | Winchester, VA |