In an AP \(a=12\) and \(d=\frac{7}{2}\). What is \(a_{15}\)?
Answer and explanation
Correct answer: 61
The \(n\)th term of an AP is \(a_n=a+(n-1)d\). Therefore, \(a_{15}=12+(15-1)\times\frac{7}{2}=12+14\times\frac{7}{2}=12+49=61\). Hence, 61 is correct. A value such as 59 can result from using an incorrect number of common differences. Exam tip: always use \(n-1\), not \(n\), in the nth-term formula.
Frequently asked questions
What is the correct answer to this question?
61
Why is this the correct answer?
The \(n\)th term of an AP is \(a_n=a+(n-1)d\). Therefore, \(a_{15}=12+(15-1)\times\frac{7}{2}=12+14\times\frac{7}{2}=12+49=61\). Hence, 61 is correct. A value such as 59 can result from using an incorrect number of common differences. Exam tip: always use \(n-1\), not \(n\), in the nth-term formula.
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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