If (S_{25}=1225) and (S_{24}=1128), what is the (25)th term?
Answer and explanation
Correct answer: 97
In an AP, the nth term can be found using \(a_n=S_n-S_{n-1}\). Therefore, \(a_{25}=S_{25}-S_{24}=1225-1128=97\). Hence, the correct answer is 97. For example, 96 is incorrect because it is not the difference between \(S_{25}\) and \(S_{24}\). Exam tip: The difference between two consecutive partial sums always gives the newly added term.
Frequently asked questions
What is the correct answer to this question?
97
Why is this the correct answer?
In an AP, the nth term can be found using \(a_n=S_n-S_{n-1}\). Therefore, \(a_{25}=S_{25}-S_{24}=1225-1128=97\). Hence, the correct answer is 97. For example, 96 is incorrect because it is not the difference between \(S_{25}\) and \(S_{24}\). Exam tip: The difference between two consecutive partial sums always gives the newly added term.
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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