In the sequence (2,6,12,20,\ldots), (a_n=n(n+1)). Which term is (210)?
Answer and explanation
Correct answer: (14)th
The formula \(a_n=n(n+1)\) says that the \(n\)-th term is the product of two consecutive positive integers, \(n\) and \(n+1\). To find which term equals 210, we need to solve \(n(n+1)=210\). We can look for two consecutive factors of 210. The pair 14 and 15 works because both are consecutive and their product is 210.
Thus \(n=14\), so 210 is the 14th term and option A is correct. Substitution verifies it: \(a_{14}=14(14+1)=14\times15=210\). The 15th term would instead be \(15\times16=240\), so option B is not correct. The index is the first factor \(n\), not the second factor \(n+1\).
Frequently asked questions
What is the correct answer to this question?
(14)th
Why is this the correct answer?
The formula \(a_n=n(n+1)\) says that the \(n\)-th term is the product of two consecutive positive integers, \(n\) and \(n+1\). To find which term equals 210, we need to solve \(n(n+1)=210\). We can look for two consecutive factors of 210. The pair 14 and 15 works because both are consecutive and their product is 210.
Thus \(n=14\), so 210 is the 14th term and option A is correct. Substitution verifies it: \(a_{14}=14(14+1)=14\times15=210\). The 15th term would instead be \(15\times16=240\), so option B is not correct. The index is the first factor \(n\), not the second factor \(n+1\).
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Sequences.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
