What is the general term of the sequence 3, 8, 13, 18, …?

Look at how the sequence 3, 8, 13, 18, … grows. From 3 to 8 is +5, from 8 to 13 is +5, from 13 to 18 is +5. The common difference is d = 5, so the general term will contain 5n.

Use aₙ = a + (n − 1)d with a = 3 and d = 5: aₙ = 3 + (n − 1)5 = 3 + 5n − 5 = 5n − 2.

Test it: when n = 1, 5(1) − 2 = 3 ✓; when n = 2, 5(2) − 2 = 8 ✓; when n = 4, 5(4) − 2 = 18 ✓. So the general term is 5n − 2. (5n alone would give 5, 10, 15, and 5n + 2 would give 7, 12, 17 — both wrong.)