WAEC 2024 Mathematics · Question 40

The first term of an Arithmetic Progression (A.P) is 2 and the last term is 29. If the common difference is 3, how many terms are in the A.P.?

Options

A.8
B.9
C.10
D.11

Answer: C. 10

Explanation written with AI and checked against the answer key

Analyze the question We are given an A.P. with first term a = 2, last term l = 29, and common difference d = 3. We need the number of terms, n. Concept The nth term of an A.P. is: Tₙ = a + (n − 1)d Solution Set the last term equal to 29: 29 = 2 + (n − 1)(3) 29 − 2 = 3(n − 1) 27 = 3(n − 1) n − 1 = 9 n = 10 Check: The terms are 2, 5, 8, 11, 14, 17, 20, 23, 26, 29. Counting them gives 10 terms, and the last one is 29. ✓ Answer: C. 10 Tip: For an A.P., the number of terms is n = (l − a)/d + 1. Here that is (29 − 2)/3 + 1 = 9 + 1 = 10. Do not forget the "+1", because the difference only counts the gaps between terms, and there is one more term than there are gaps. Choosing 9 is the usual mistake.

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