According to the recursive rule in the sequence (4, 7, 10, 13, ...), what is the next term?
Answer and explanation
Correct answer: 16
The governing concept is a recursive rule, in which each term is obtained from the preceding term. Examine the consecutive changes in the sequence: 7 − 4 = 3, 10 − 7 = 3, and 13 − 10 = 3. Since the same difference occurs each time, the recursive rule is “add 3 to the previous term.” Applying this rule to the last known term gives 13 + 3 = 16. Therefore, option C is correct. This sequence is also an arithmetic progression with common difference 3, although the question specifically highlights the step-by-step recursive construction. Option A, 14, changes by only 1; option B, 15, changes by 2; and option D, 17, changes by 4, so none preserves the established rule.
Frequently asked questions
What is the correct answer to this question?
16
Why is this the correct answer?
The governing concept is a recursive rule, in which each term is obtained from the preceding term. Examine the consecutive changes in the sequence: 7 − 4 = 3, 10 − 7 = 3, and 13 − 10 = 3. Since the same difference occurs each time, the recursive rule is “add 3 to the previous term.” Applying this rule to the last known term gives 13 + 3 = 16. Therefore, option C is correct. This sequence is also an arithmetic progression with common difference 3, although the question specifically highlights the step-by-step recursive construction. Option A, 14, changes by only 1; option B, 15, changes by 2; and option D, 17, changes by 4, so none preserves the established rule.
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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