If (a_n=3n+2), what is (a_{n+3}-a_n)?
Answer and explanation
Correct answer: (9)
The governing concept is evaluating the same explicit sequence rule at two related indices and subtracting. First, aₙ₊₃ = 3(n + 3) + 2 = 3n + 9 + 2 = 3n + 11. Therefore aₙ₊₃ − aₙ = (3n + 11) − (3n + 2) = 9. Hence option A is correct. Another way to see this is that each increase of one in the index raises the term by 3; increasing the index by 3 raises it by 3 × 3 = 9. The distractors 6 and 3 reflect using the wrong index change or counting only one step, while 11 is the constant part of aₙ₊₃ rather than the required difference.
Frequently asked questions
What is the correct answer to this question?
(9)
Why is this the correct answer?
The governing concept is evaluating the same explicit sequence rule at two related indices and subtracting. First, aₙ₊₃ = 3(n + 3) + 2 = 3n + 9 + 2 = 3n + 11. Therefore aₙ₊₃ − aₙ = (3n + 11) − (3n + 2) = 9. Hence option A is correct. Another way to see this is that each increase of one in the index raises the term by 3; increasing the index by 3 raises it by 3 × 3 = 9. The distractors 6 and 3 reflect using the wrong index change or counting only one step, while 11 is the constant part of aₙ₊₃ rather than the required difference.
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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