What is the (40)th term of the AP (14,14,14,14,\ldots)?
Answer and explanation
Correct answer: 14
The first term is \(a=14\) and the common difference is \(d=14-14=0\). Hence, \(a_n=a+(n-1)d=14+(n-1)\times 0=14\). Therefore, the 40th term is 14. The value 560 is \(14\times 40\), but an AP term is not found by multiplying the first term by its position. Exam tip: if all terms of an AP are equal, its common difference is 0 and every term equals the first term.
Frequently asked questions
What is the correct answer to this question?
14
Why is this the correct answer?
The first term is \(a=14\) and the common difference is \(d=14-14=0\). Hence, \(a_n=a+(n-1)d=14+(n-1)\times 0=14\). Therefore, the 40th term is 14. The value 560 is \(14\times 40\), but an AP term is not found by multiplying the first term by its position. Exam tip: if all terms of an AP are equal, its common difference is 0 and every term equals the first term.
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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