If (a_1=22) and (d=13), what is the (5)th term?
Answer and explanation
Correct answer: 74
The nth term of an AP is \(a_n=a_1+(n-1)d\). Thus, \(a_5=22+(5-1)\times13=22+52=74\). Therefore, 74 is correct. The value 76 results from incorrectly adding \(5d\); the common difference is added only four times to reach the fifth term. Exam tip: always use \(n-1\), not \(n\), in the formula.
Frequently asked questions
What is the correct answer to this question?
74
Why is this the correct answer?
The nth term of an AP is \(a_n=a_1+(n-1)d\). Thus, \(a_5=22+(5-1)\times13=22+52=74\). Therefore, 74 is correct. The value 76 results from incorrectly adding \(5d\); the common difference is added only four times to reach the fifth term. Exam tip: always use \(n-1\), not \(n\), in the 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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