What is the general term of the sequence (13, 26, 39, 52, …)?
Answer and explanation
Correct answer: aₙ = 13n
Every term is a consecutive multiple of 13: 13 = 13×1, 26 = 13×2, 39 = 13×3, and 52 = 13×4. Therefore the term in position n is aₙ = 13n, so option A is correct. The same conclusion follows from the arithmetic-sequence formula. The first term is 13 and the common difference is also 13, so aₙ = 13 + (n − 1)13 = 13n. Option B gives 14 for the first term, option C gives 13 initially but then 25 rather than 26, and option D gives 26 for the first term. Checking more than one position prevents a formula from being accepted merely because it matches the first term.
Frequently asked questions
What is the correct answer to this question?
aₙ = 13n
Why is this the correct answer?
Every term is a consecutive multiple of 13: 13 = 13×1, 26 = 13×2, 39 = 13×3, and 52 = 13×4. Therefore the term in position n is aₙ = 13n, so option A is correct. The same conclusion follows from the arithmetic-sequence formula. The first term is 13 and the common difference is also 13, so aₙ = 13 + (n − 1)13 = 13n. Option B gives 14 for the first term, option C gives 13 initially but then 25 rather than 26, and option D gives 26 for the first term. Checking more than one position prevents a formula from being accepted merely because it matches the first term.
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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