What is the (9)th term of the AP (18,28,38,48,\ldots)?
Answer and explanation
Correct answer: 98
For this AP, the first term is \(a=18\) and the common difference is \(d=28-18=10\). The \(n\)th term is \(a_n=a+(n-1)d\). Therefore, \(a_9=18+(9-1)\times10=18+80=98\). The answer 108 would result from adding 9 differences, but only 8 differences are added to reach the 9th term. Exam tip: always use \(n-1\), not \(n\), in the nth-term formula.
Frequently asked questions
What is the correct answer to this question?
98
Why is this the correct answer?
For this AP, the first term is \(a=18\) and the common difference is \(d=28-18=10\). The \(n\)th term is \(a_n=a+(n-1)d\). Therefore, \(a_9=18+(9-1)\times10=18+80=98\). The answer 108 would result from adding 9 differences, but only 8 differences are added to reach the 9th term. 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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