If aₙ = 11n − 15, what is a₂ᵣ₋₁?
Answer and explanation
Correct answer: 22r − 26
The governing idea is substitution into an explicit general term. The formula aₙ = 11n − 15 is valid for any permitted index, so replace the index n by the entire expression 2r − 1. Thus a₂ᵣ₋₁ = 11(2r − 1) − 15. Distributing 11 gives 22r − 11 − 15, and combining constants gives 22r − 26. Therefore option A is correct. The complete index must be substituted; replacing it only by r would produce the wrong expression. Option B forgets to subtract the contribution from −1, option C uses 11r instead of 22r, and option D adds rather than correctly combines the constant terms.
Frequently asked questions
What is the correct answer to this question?
22r − 26
Why is this the correct answer?
The governing idea is substitution into an explicit general term. The formula aₙ = 11n − 15 is valid for any permitted index, so replace the index n by the entire expression 2r − 1. Thus a₂ᵣ₋₁ = 11(2r − 1) − 15. Distributing 11 gives 22r − 11 − 15, and combining constants gives 22r − 26. Therefore option A is correct. The complete index must be substituted; replacing it only by r would produce the wrong expression. Option B forgets to subtract the contribution from −1, option C uses 11r instead of 22r, and option D adds rather than correctly combines the constant terms.
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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