Which is the correct rule for the sequence (\frac{3}{7},\frac{6}{12},\frac{9}{17},\frac{12}{22},\ldots)?
Answer and explanation
Correct answer: (a_n=\frac{3n}{5n+2})
The rule of a sequence can be found by observing how the numerator and denominator depend on n. The numerators are 3, 6, 9, and 12, which are exactly 3n for n=1, 2, 3, and 4. The denominators are 7, 12, 17, and 22. They increase by 5, and the expression 5n+2 gives these values. Thus the general term is \(a_n=\frac{3n}{5n+2}\), which is option A.
Substitution verifies the answer: at n=1, \(\frac{3}{7}\) is obtained; at n=2, \(\frac{6}{12}\); at n=3, \(\frac{9}{17}\); and at n=4, \(\frac{12}{22}\). Option C uses the wrong denominator pattern, and options B and D do not produce the numerators 3n. Both parts of the fraction must match the sequence.
Frequently asked questions
What is the correct answer to this question?
(a_n=\frac{3n}{5n+2})
Why is this the correct answer?
The rule of a sequence can be found by observing how the numerator and denominator depend on n. The numerators are 3, 6, 9, and 12, which are exactly 3n for n=1, 2, 3, and 4. The denominators are 7, 12, 17, and 22. They increase by 5, and the expression 5n+2 gives these values. Thus the general term is \(a_n=\frac{3n}{5n+2}\), which is option A.
Substitution verifies the answer: at n=1, \(\frac{3}{7}\) is obtained; at n=2, \(\frac{6}{12}\); at n=3, \(\frac{9}{17}\); and at n=4, \(\frac{12}{22}\). Option C uses the wrong denominator pattern, and options B and D do not produce the numerators 3n. Both parts of the fraction must match the sequence.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Explicit or general rule.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
