If aₙ = 9n − 11, what is a₂ₖ₊₃?
Answer and explanation
Correct answer: 18k + 16
The governing concept is substitution of a composite index into an explicit sequence formula. The rule is aₙ = 9n − 11, and the requested index is 2k + 3. Replace the entire n by 2k + 3: a₂ₖ₊₃ = 9(2k + 3) − 11. Distributing 9 gives 18k + 27 − 11, which simplifies to 18k + 16. Therefore option A is correct. Option B stops before subtracting 11, option C incorrectly multiplies only k by 9, and option D substitutes the expression incompletely. Keeping the complete index inside parentheses is essential to avoid these errors.
Frequently asked questions
What is the correct answer to this question?
18k + 16
Why is this the correct answer?
The governing concept is substitution of a composite index into an explicit sequence formula. The rule is aₙ = 9n − 11, and the requested index is 2k + 3. Replace the entire n by 2k + 3: a₂ₖ₊₃ = 9(2k + 3) − 11. Distributing 9 gives 18k + 27 − 11, which simplifies to 18k + 16. Therefore option A is correct. Option B stops before subtracting 11, option C incorrectly multiplies only k by 9, and option D substitutes the expression incompletely. Keeping the complete index inside parentheses is essential to avoid these errors.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: nth term.
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