Mathematics is all about finding patterns. Begin learning to spot patterns in numbers today, and maybe one day you can solve a big mathematical problem—like Maninder Agarwal, Neeraj Kayal, and Nitin Saxena, computer scientists at IIT, Kanpur. These mathematical stars have just announced a new algorithm, by which they can tell whether a number is a prime number. An implementation of this algorithm will mean that everyone will have to re-look at computer programs used to keep messages transferred on the Internet confidential.

In today’s activity, find the next three terms in the following sequences.

Q1. $1, 3, 5, 7,\dots $

Q2. $2, 4, 6, 8, \dots $

Q3. $1, 4, 9, 16, \dots $

Q4. $2, 3, 5, 7, 11, 13, 17, \dots $

Q5. $1, 2, 4, 8, 16, \dots $

Q6. $1, 4, 1, 4, 2, \dots $

Q7. $3, 6, 9, 12, 15, 18, \dots $

Q8. $0, 3, 8, 15, 24, \dots $

Q9. $0, 1, 1, 2, 3, 5, 8, \dots $

Q10. $1, 3, 6, 10, 15, 21, \dots $

Q11. $2, 8, 20, 40, 70, \dots $

Q12. $1, 5, 14, 20, 55, \dots $