WAEC 2014 Mathematics · Question 27

Find the number of term in the Arithmetic Progression(A.P) 2, -9, -20,...-141.

Options

A.11
B.12
C.13
D.14

Answer: D. 14

Explanation written with AI and checked against the answer key

Analyze the question: We have an A.P. with first term a = 2, common difference d = -9 - 2 = -11, and last term l = -141. We need the number of terms, n. Concept: The nth term of an A.P. is Tₙ = a + (n - 1)d Solution: -141 = 2 + (n - 1)(-11) -141 - 2 = -11(n - 1) -143 = -11(n - 1) n - 1 = 143 ÷ 11 = 13 n = 14 Check: Tₙ = 2 - 11(13) = 2 - 143 = -141 ✓ The sequence goes 2, -9, -20, -31, -42, -53, -64, -75, -86, -97, -108, -119, -130, -141. That's 14 terms. Tip: For "number of terms" questions, use n = (l - a)/d + 1. Here, (-141 - 2)/(-11) + 1 = 13 + 1 = 14. Always add the 1, because the subtraction counts only the gaps between terms, not the terms themselves. Also watch the signs: dividing a negative by a negative gives a positive.

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