Which explicit rule is correct for the sequence (5, 10, 15, 20, …)?
Answer and explanation
Correct answer: aₙ = 5n
The governing concept is an explicit rule, where the nth term is obtained directly from n. The displayed sequence is made of consecutive multiples of 5: 5×1, 5×2, 5×3 and 5×4. Thus the natural rule is aₙ = 5n. Checking it gives a₁ = 5, a₂ = 10, a₃ = 15 and a₄ = 20, exactly as required. Therefore option A is correct. The rule n + 5 produces 6 as the first term, 4n produces 4 as the first term, and 5n − 1 produces 4 as the first term; each fails immediately at n = 1. The constant difference is 5, but that fact must still be combined with the correct first-term position to obtain 5n.
Frequently asked questions
What is the correct answer to this question?
aₙ = 5n
Why is this the correct answer?
The governing concept is an explicit rule, where the nth term is obtained directly from n. The displayed sequence is made of consecutive multiples of 5: 5×1, 5×2, 5×3 and 5×4. Thus the natural rule is aₙ = 5n. Checking it gives a₁ = 5, a₂ = 10, a₃ = 15 and a₄ = 20, exactly as required. Therefore option A is correct. The rule n + 5 produces 6 as the first term, 4n produces 4 as the first term, and 5n − 1 produces 4 as the first term; each fails immediately at n = 1. The constant difference is 5, but that fact must still be combined with the correct first-term position to obtain 5n.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Explicit or general rule.
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