In an AP, (a_{21}=a_9+132) and (a_9=54). What is (a_{57})?
Answer and explanation
Correct answer: 582
In an AP, the difference between two terms equals the difference in their positions multiplied by the common difference. Thus, \(a_{21}-a_9=12d=132\), so \(d=11\). Now, \(a_{57}=a_9+(57-9)d=54+48\times11=582\). Therefore, option C is correct. The value 570 does not include the full increase of 48 common differences. Exam tip: When moving from one known term to another, use the difference between their term numbers.
Frequently asked questions
What is the correct answer to this question?
582
Why is this the correct answer?
In an AP, the difference between two terms equals the difference in their positions multiplied by the common difference. Thus, \(a_{21}-a_9=12d=132\), so \(d=11\). Now, \(a_{57}=a_9+(57-9)d=54+48\times11=582\). Therefore, option C is correct. The value 570 does not include the full increase of 48 common differences. Exam tip: When moving from one known term to another, use the difference between their term numbers.
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.
