If the sum of an AP is (S_n=3n^2+5n), find the (22)nd term.
Answer and explanation
Correct answer: 134
To find the nth term from the sum of an AP, use \(a_n=S_n-S_{n-1}\). Thus, \(a_{22}=S_{22}-S_{21}\). Here, \(S_{22}=3(22)^2+5(22)=1562\) and \(S_{21}=3(21)^2+5(21)=1428\). Therefore, \(a_{22}=1562-1428=134\). Option 131 is not correct because it does not result from the correct difference between \(S_{22}\) and \(S_{21}\). Exam tip: When \(S_n\) is given, obtain the nth term by subtracting \(S_{n-1}\) from \(S_n\).
Frequently asked questions
What is the correct answer to this question?
134
Why is this the correct answer?
To find the nth term from the sum of an AP, use \(a_n=S_n-S_{n-1}\). Thus, \(a_{22}=S_{22}-S_{21}\). Here, \(S_{22}=3(22)^2+5(22)=1562\) and \(S_{21}=3(21)^2+5(21)=1428\). Therefore, \(a_{22}=1562-1428=134\). Option 131 is not correct because it does not result from the correct difference between \(S_{22}\) and \(S_{21}\). Exam tip: When \(S_n\) is given, obtain the nth term by subtracting \(S_{n-1}\) from \(S_n\).
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Arithmetic Progressions (AP). Topic: Finding the sum of the first $n$ terms of an AP.
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