A sequence begins 5, 9, 13, 17 and keeps the same pattern. What is its fifteenth term?

1. Check the gaps first: 9 minus 5 is 4, 13 minus 9 is 4 and 17 minus 13 is 4. 2. The common difference is 4, so this is a linear sequence. 3. For a linear sequence the common difference is the coefficient of the position number. 4. Four times the position number gives 4, 8, 12, 16 for the first four positions. 5. Each of those is one less than the matching term, so add 1. 6. The rule is four times the position number, plus 1. 7. For position fifteen that gives 60 plus 1, which is 61. 8. Answering 60 stops at four times fifteen and forgets the constant. _Source: Siyavula Mathematics Grade 11 (Everything Maths, CC BY 4.0), Chapter 3: Number patterns_