If the sum of an AP is (S_n=4n^2+9n), find the (27)th term.
Answer and explanation
Correct answer: 221
To find the nth term of an AP from its sum, use \(a_n=S_n-S_{n-1}\). Here, \(a_n=(4n^2+9n)-[4(n-1)^2+9(n-1)]=8n+5\). Therefore, \(a_{27}=8\times27+5=221\). Hence, 221 is the correct option. The value 223 may result from an error of 2 during simplification. Exam tip: When \(S_n\) is given, obtain a term by subtracting two consecutive partial sums.
Frequently asked questions
What is the correct answer to this question?
221
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, \(a_n=(4n^2+9n)-[4(n-1)^2+9(n-1)]=8n+5\). Therefore, \(a_{27}=8\times27+5=221\). Hence, 221 is the correct option. The value 223 may result from an error of 2 during simplification. Exam tip: When \(S_n\) is given, obtain a term by subtracting two consecutive partial sums.
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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