If the (19)th term of the AP (z,z+5,z+10,\ldots) is (112), what is (z)?
Answer and explanation
Correct answer: 22
Here, the first term is \(a=z\) and the common difference is \(d=5\). The \(n\)th term is \(a_n=a+(n-1)d\). Thus, \(112=z+(19-1)\times5=z+90\), so \(z=22\). If 20 were used, the 19th term would be \(20+90=110\), not 112. Exam tip: always use \(n-1\), not \(n\), in the nth-term formula.
Frequently asked questions
What is the correct answer to this question?
22
Why is this the correct answer?
Here, the first term is \(a=z\) and the common difference is \(d=5\). The \(n\)th term is \(a_n=a+(n-1)d\). Thus, \(112=z+(19-1)\times5=z+90\), so \(z=22\). If 20 were used, the 19th term would be \(20+90=110\), not 112. 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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