A sequence runs 3, 8, 17, 30 and continues in the same way. What is the next term?

1. Find the first differences: 8 minus 3 is 5, 17 minus 8 is 9 and 30 minus 17 is 13. 2. Those first differences are 5, 9 and 13, so they are not constant. 3. Find the second differences: 9 minus 5 is 4 and 13 minus 9 is 4. 4. The second difference is a constant 4, so this is a quadratic sequence. 5. The next first difference is therefore 13 plus 4, which is 17. 6. Add that to the last term: 30 plus 17 is 47. 7. Answering 43 repeats the first difference of 13 without adding the second difference. 8. Answering 51 adds 21, which uses two extra steps of the second difference. _Source: Siyavula Mathematics Grade 11 (Everything Maths, CC BY 4.0), Chapter 3: Number patterns_