What is the nth term of the arithmetic progression 8, 17, 26, 35, ...?

Correct answer: aₙ = 9n − 1

Direct answer: option A, aₙ = 9n − 1. For an AP, aₙ = a + (n − 1)d. The first term is a = 8 and the common difference is d = 17 − 8 = 9. Substitution gives aₙ = 8 + (n − 1)9 = 8 + 9n − 9 = 9n − 1. Check the rule: n = 1 gives 8, n = 2 gives 17, and n = 3 gives 26, exactly the listed terms. B gives 17 when n = 1, so it fails immediately. C also gives 17 at n = 1 and has the wrong constant term. D has a difference of 1 between successive values, not 9. A useful memory cue is first term plus (number of jumps × common difference): there are n − 1 jumps before the nth term.