What is the (15)th term of the AP (4,12,20,28,\ldots)?
Answer and explanation
Correct answer: \(116\)
The first term is \(a=4\), and the common difference is \(d=12-4=8\). The \(n\)th term is \(a_n=a+(n-1)d\). Therefore, \(a_{15}=4+(15-1)\times8=4+112=116\). Hence, \(116\) is correct. \(120\) results from incorrectly using \(n\) instead of \((n-1)\). Exam tip: put \(n=1\) in the formula to check that it gives \(a_1=a\).
Frequently asked questions
What is the correct answer to this question?
\(116\)
Why is this the correct answer?
The first term is \(a=4\), and the common difference is \(d=12-4=8\). The \(n\)th term is \(a_n=a+(n-1)d\). Therefore, \(a_{15}=4+(15-1)\times8=4+112=116\). Hence, \(116\) is correct. \(120\) results from incorrectly using \(n\) instead of \((n-1)\). Exam tip: put \(n=1\) in the formula to check that it gives \(a_1=a\).
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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