A sequence begins 3, 7, 11, 15 and carries on in the same way. What is its twentieth term?

1. Check the gaps first: 7 minus 3 is 4, 11 minus 7 is 4 and 15 minus 11 is 4. 2. The common difference is therefore 4, so the sequence is linear. 3. For a linear sequence the general formula has the common difference as 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 more than the matching term, so subtract 1. 6. The general formula is four times the position number, minus 1. 7. For position twenty that gives 80 minus 1, which is 79. 8. Answering 80 stops at four times twenty and forgets the constant. _Source: Siyavula Mathematics Grade 10 (Everything Maths, CC BY 4.0), Chapter 3: Number patterns_