If (a_{3n+2}=148), (a_{n+2}=52), and (d=12), what is (n)?
Answer and explanation
Correct answer: \(4\)
In an AP, \(a_p-a_q=(p-q)d\). Hence, \(a_{3n+2}-a_{n+2}=[(3n+2)-(n+2)]d=2nd\). Therefore, \(148-52=2n\times12\), so \(96=24n\) and \(n=4\). If \(n=3\), the difference would be \(72\), not the given difference \(96\). Exam tip: When two terms are given, first find the difference between their subscripts.
Frequently asked questions
What is the correct answer to this question?
\(4\)
Why is this the correct answer?
In an AP, \(a_p-a_q=(p-q)d\). Hence, \(a_{3n+2}-a_{n+2}=[(3n+2)-(n+2)]d=2nd\). Therefore, \(148-52=2n\times12\), so \(96=24n\) and \(n=4\). If \(n=3\), the difference would be \(72\), not the given difference \(96\). Exam tip: When two terms are given, first find the difference between their subscripts.
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.
