NECO 2008 Mathematics · Question 37

If the 3rd and the 5th terms of an A.P are 6 and 10 respectively, find the 1st term and the common difference respectively.

Options

A.1, 2
B.2, 2
C.2, 3
D.3, 2
E.3,3

Answer: B. 2, 2

Explanation written with AI and checked against the answer key

Analyze the question We're told the 3rd term of an arithmetic progression (A.P) is 6 and the 5th term is 10. We need the first term (a) and the common difference (d). Concept The nth term of an A.P is: Tₙ = a + (n − 1)d Solution 3rd term: a + 2d = 6 ... (i) 5th term: a + 4d = 10 ... (ii) Subtract (i) from (ii): (a + 4d) − (a + 2d) = 10 − 6 2d = 4 d = 2 Substitute d = 2 into (i): a + 2(2) = 6 a + 4 = 6 a = 2 Check: The terms are 2, 4, 6, 8, 10. The 3rd term is 6 and the 5th term is 10. ✓ Answer: First term = 2, common difference = 2, which is option B. Tip: When you're given two terms of an A.P, subtract the equations to eliminate a and find d first. The gap between the 3rd and 5th terms is 2 steps, so 2d = 10 − 6 = 4, which gives d = 2 immediately. Then count back from the 3rd term: 6 − 2 = 4 (2nd term), 4 − 2 = 2 (1st term).

AI can make mistakes. Report anything that looks wrong.