If (a_n=4n+r) and (a_{15}=83), what is (a_{41})?
Answer and explanation
Correct answer: 187
Given \(a_n=4n+r\). Substituting \(n=15\), \(83=4\times15+r=60+r\), so \(r=23\). Hence, \(a_{41}=4\times41+23=164+23=187\). Therefore, option C is correct. The value \(183\) would result from using an incorrect value of \(r\). Exam tip: first find the unknown constant from the given term, then substitute the required value of \(n\).
Frequently asked questions
What is the correct answer to this question?
187
Why is this the correct answer?
Given \(a_n=4n+r\). Substituting \(n=15\), \(83=4\times15+r=60+r\), so \(r=23\). Hence, \(a_{41}=4\times41+23=164+23=187\). Therefore, option C is correct. The value \(183\) would result from using an incorrect value of \(r\). Exam tip: first find the unknown constant from the given term, then substitute the required value of \(n\).
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.
