What is the (22)nd term of the AP (31,34,37,40,\ldots)?
Answer and explanation
Correct answer: 94
For this AP, the first term is \(a=31\) and the common difference is \(d=34-31=3\). Use \(a_n=a+(n-1)d\). Thus, \(a_{22}=31+(22-1)\times3=31+63=94\). Therefore, 94 is the correct answer. Choosing 91 means adding only 20 common differences, so it is the 21st 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?
94
Why is this the correct answer?
For this AP, the first term is \(a=31\) and the common difference is \(d=34-31=3\). Use \(a_n=a+(n-1)d\). Thus, \(a_{22}=31+(22-1)\times3=31+63=94\). Therefore, 94 is the correct answer. Choosing 91 means adding only 20 common differences, so it is the 21st 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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