If the sum of an AP is (S_n=5n^2-4n), find the (35)th term.
Answer and explanation
Correct answer: 341
For an AP, the \(n\)th term is \(a_n=S_n-S_{n-1}\). Therefore, \(a_{35}=S_{35}-S_{34}\). Here, \(S_{35}=5(35)^2-4(35)=5985\) and \(S_{34}=5(34)^2-4(34)=5644\). Hence, \(a_{35}=5985-5644=341\). Option 336 does not give the correct difference for \(n=35\). Exam tip: When \(S_n\) is given, find an individual term using \(S_n-S_{n-1}\).
Frequently asked questions
What is the correct answer to this question?
341
Why is this the correct answer?
For an AP, the \(n\)th term is \(a_n=S_n-S_{n-1}\). Therefore, \(a_{35}=S_{35}-S_{34}\). Here, \(S_{35}=5(35)^2-4(35)=5985\) and \(S_{34}=5(34)^2-4(34)=5644\). Hence, \(a_{35}=5985-5644=341\). Option 336 does not give the correct difference for \(n=35\). Exam tip: When \(S_n\) is given, find an individual term using \(S_n-S_{n-1}\).
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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