What is the (22)nd term of the AP (1,8,15,22,\ldots)?
Answer and explanation
Correct answer: 148
For this AP, the first term is \(a=1\) and the common difference is \(d=8-1=7\). The \(n\)th term is given by \(a_n=a+(n-1)d\). Thus, \(a_{22}=1+(22-1)\times7=1+147=148\). Therefore, 148 is correct. A value such as 146 can result from counting the terms or the common difference incorrectly. Exam tip: for the \(n\)th term, use \((n-1)d\), not \(nd\).
Frequently asked questions
What is the correct answer to this question?
148
Why is this the correct answer?
For this AP, the first term is \(a=1\) and the common difference is \(d=8-1=7\). The \(n\)th term is given by \(a_n=a+(n-1)d\). Thus, \(a_{22}=1+(22-1)\times7=1+147=148\). Therefore, 148 is correct. A value such as 146 can result from counting the terms or the common difference incorrectly. Exam tip: for the \(n\)th term, use \((n-1)d\), not \(nd\).
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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