What is the (25)th term of the AP (100,97,94,91,\ldots)?
Answer and explanation
Correct answer: 28
In this AP, the first term is \(a=100\) and the common difference is \(d=97-100=-3\). The \(n\)th term is given by \(a_n=a+(n-1)d\). Therefore, \(a_{25}=100+(25-1)(-3)=100-72=28\). Hence, 28 is correct. Getting 30 may result from using an incorrect number of common differences instead of 24. Exam tip: for the \(n\)th term, always use \(n-1\) differences.
Frequently asked questions
What is the correct answer to this question?
28
Why is this the correct answer?
In this AP, the first term is \(a=100\) and the common difference is \(d=97-100=-3\). The \(n\)th term is given by \(a_n=a+(n-1)d\). Therefore, \(a_{25}=100+(25-1)(-3)=100-72=28\). Hence, 28 is correct. Getting 30 may result from using an incorrect number of common differences instead of 24. Exam tip: for the \(n\)th term, always use \(n-1\) differences.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Arithmetic Progressions (AP). Topic: Finding the $n$th term of an AP.
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