If the sum of an AP is (S_n=2n^2+7n), find the (18)th term.
Answer and explanation
Correct answer: 77
To find the nth term of an AP from its sum, use \(a_n=S_n-S_{n-1}\). Here, \(S_{18}=2(18)^2+7(18)=774\) and \(S_{17}=2(17)^2+7(17)=697\). Therefore, \(a_{18}=S_{18}-S_{17}=774-697=77\). The values 75, 79, and 81 do not equal this required difference. Exam tip: When \(S_n\) is given, obtain the nth term by calculating \(S_n-S_{n-1}\).
Frequently asked questions
What is the correct answer to this question?
77
Why is this the correct answer?
To find the nth term of an AP from its sum, use \(a_n=S_n-S_{n-1}\). Here, \(S_{18}=2(18)^2+7(18)=774\) and \(S_{17}=2(17)^2+7(17)=697\). Therefore, \(a_{18}=S_{18}-S_{17}=774-697=77\). The values 75, 79, and 81 do not equal this required difference. Exam tip: When \(S_n\) is given, obtain the nth term by calculating \(S_n-S_{n-1}\).
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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