If (a_{2n+1}=89), (a_{n+1}=41), and (d=6), what is (n)?
Answer and explanation
Correct answer: 8
In an AP, the difference between two terms equals the difference of their indices multiplied by the common difference. Thus, \(a_{2n+1}-a_{n+1}=[(2n+1)-(n+1)]d=nd\). Hence \(89-41=6n\), so \(48=6n\) and \(n=8\). If \(n=7\), the difference would be \(42\), not 48. Exam tip: first find the difference between the term indices; here it is \(n\).
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
In an AP, the difference between two terms equals the difference of their indices multiplied by the common difference. Thus, \(a_{2n+1}-a_{n+1}=[(2n+1)-(n+1)]d=nd\). Hence \(89-41=6n\), so \(48=6n\) and \(n=8\). If \(n=7\), the difference would be \(42\), not 48. Exam tip: first find the difference between the term indices; here it is \(n\).
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Arithmetic Progressions (AP). Topic: Finding the $n$th term of an AP.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
