If \(a_n=kn-8\) and \(a_{19}-a_7=96\), what is \(a_{24}\)?
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Answer and explanation
Correct answer: 184
Given \(a_n=kn-8\), we have \(a_{19}=19k-8\) and \(a_7=7k-8\). Thus, \(a_{19}-a_7=(19k-8)-(7k-8)=12k=96\), so \(k=8\). Now \(a_{24}=24k-8=24\times8-8=184\). Hence, 184 is correct. Exam tip: when subtracting two terms, the constant term \(-8\) cancels out.
Frequently asked questions
What is the correct answer to this question?
184
Why is this the correct answer?
Given \(a_n=kn-8\), we have \(a_{19}=19k-8\) and \(a_7=7k-8\). Thus, \(a_{19}-a_7=(19k-8)-(7k-8)=12k=96\), so \(k=8\). Now \(a_{24}=24k-8=24\times8-8=184\). Hence, 184 is correct. Exam tip: when subtracting two terms, the constant term \(-8\) cancels out.
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.
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