WAEC 2019 Mathematics · Question 39

If 6, P, and 14 are consecutive terms in an Arithmetic Progression (AP), find the value of P.

Options

A.9
B.10
C.6
D.8

Answer: B. 10

Explanation written with AI and checked against the answer key

Analyze the question: Three numbers 6, P, 14 are consecutive terms of an AP. In an AP, the difference between consecutive terms is constant, so P is the middle term, i.e. the average of its neighbours. Concept: If a, b, c are consecutive terms of an AP, then b − a = c − b, so b = (a + c)/2. Solution: Common difference condition: P − 6 = 14 − P 2P = 20 P = 10 Check: The sequence 6, 10, 14 has a common difference of 4 each time (10 − 6 = 4, 14 − 10 = 4). ✓ Answer: B (10) Tip: When you see three consecutive AP terms with the middle one missing, just find the average of the other two: (6 + 14)/2 = 10. This saves time in the exam.

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