If (a_1=19) and (a_{11}=a_1+80), what is (a_{31})?
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Answer and explanation
Correct answer: 259
In an AP, \(a_{11}=a_1+10d\). Given \(a_{11}=a_1+80\), we get \(10d=80\), so \(d=8\). Therefore, \(a_{31}=a_1+30d=19+30\times8=259\). The value 251 would result from using an incorrect term position. Exam tip: in \(a_n=a_1+(n-1)d\), use \(n-1\), not \(n\).
Frequently asked questions
What is the correct answer to this question?
259
Why is this the correct answer?
In an AP, \(a_{11}=a_1+10d\). Given \(a_{11}=a_1+80\), we get \(10d=80\), so \(d=8\). Therefore, \(a_{31}=a_1+30d=19+30\times8=259\). The value 251 would result from using an incorrect term position. Exam tip: in \(a_n=a_1+(n-1)d\), use \(n-1\), not \(n\).
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.
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