Which recursive rule is correct for the sequence 5, 8, 11, 14, ...?
Answer and explanation
Correct answer: a_1 = 5, a_(n+1) = a_n + 3
A recursive rule must contain two parts: an initial value and a relationship that generates each next term from the preceding term. The first term here is 5. The successive differences are 8−5=3, 11−8=3, and 14−11=3, so the same operation is repeated each time: add 3 to the previous term. Consequently, the correct rule is a_1 = 5 and a_(n+1) = a_n + 3, which is option A. Option B uses a difference of 4 and would produce 5, 9, 13, ... . Option C starts with the second term rather than the first, and option D doubles each term, producing a completely different sequence. Both the starting value and recurrence must agree with the displayed sequence.
Frequently asked questions
What is the correct answer to this question?
a_1 = 5, a_(n+1) = a_n + 3
Why is this the correct answer?
A recursive rule must contain two parts: an initial value and a relationship that generates each next term from the preceding term. The first term here is 5. The successive differences are 8−5=3, 11−8=3, and 14−11=3, so the same operation is repeated each time: add 3 to the previous term. Consequently, the correct rule is a_1 = 5 and a_(n+1) = a_n + 3, which is option A. Option B uses a difference of 4 and would produce 5, 9, 13, ... . Option C starts with the second term rather than the first, and option D doubles each term, producing a completely different sequence. Both the starting value and recurrence must agree with the displayed sequence.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Recursive rule.
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