WAEC 2024 Mathematics · Question 29

The fourth and eighth terms of an Arithmetic Progression are 16 and 40 respectively. Find the common difference.

Options

A.- 6
B.6
C.-2
D.2

Answer: B. 6

Explanation written with AI and checked against the answer key

Analyze the question: We're given the 4th term (16) and the 8th term (40) of an AP, and we need the common difference, d. Concept: The nth term of an AP is Tₙ = a + (n − 1)d Solution: T₄ = a + 3d = 16 ... (i) T₈ = a + 7d = 40 ... (ii) Subtract (i) from (ii): 4d = 40 − 16 = 24 d = 24 ÷ 4 = 6 Check: a = 16 − 3(6) = −2. The terms are −2, 4, 10, 16, 22, 28, 34, 40. The 4th term is 16 and the 8th is 40. ✔ Tip: For any two terms Tₚ and T_q, the common difference is d = (T_q − Tₚ) ÷ (q − p). Here, (40 − 16) ÷ (8 − 4) = 6. This skips the simultaneous equations and saves time in the exam.

AI can make mistakes. Report anything that looks wrong.