JAMB 2015 Mathematics · Question 61

The first and last term of a linear sequence (AP) are 6 and 10 respectively. If the sum of the sequence is 40. Find the number of terms

Options

A.nth = 3
B.nth = 4
C.nth = 5
D.nth = 6

Answer: C. nth = 5

Explanation written with AI and checked against the answer key

Analyze the question: We're given an AP with first term a = 6, last term l = 10, and sum Sₙ = 40. We need the number of terms, n. Concept: The sum of an AP when you know the first and last terms is: Sₙ = (n/2)(a + l) Solution: Sₙ = (n/2)(a + l) 40 = (n/2)(6 + 10) 40 = (n/2)(16) 40 = 8n n = 5 Check: With n = 5, the common difference is d = (10 − 6)/(5 − 1) = 1. The terms are 6, 7, 8, 9, 10, and their sum is 6 + 7 + 8 + 9 + 10 = 40 ✓ Answer: C (n = 5) Tip: When a question gives you the first term, last term, and sum, go straight to Sₙ = (n/2)(a + l). You don't need to find d first. You can always check your answer by finding d and listing the terms, as we did above.

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