In an AP, \(a_{11}=38\) and \(a_{26}=128\). Which term will be (218)?
Answer and explanation
Correct answer: 41st
Using the two given terms, the common difference is \(d=\frac{128-38}{26-11}=\frac{90}{15}=6\). Now use \(a_n=a_{11}+(n-11)d\): \(218=38+(n-11)\times6\). Thus, \(180=6(n-11)\), so \(n-11=30\) and \(n=41\). Hence, 218 is the 41st term. The 40th term is \(212\), so it is a close but incorrect option. Exam tip: When two terms are given, first find \(d\) using the difference in their term numbers.
Frequently asked questions
What is the correct answer to this question?
41st
Why is this the correct answer?
Using the two given terms, the common difference is \(d=\frac{128-38}{26-11}=\frac{90}{15}=6\). Now use \(a_n=a_{11}+(n-11)d\): \(218=38+(n-11)\times6\). Thus, \(180=6(n-11)\), so \(n-11=30\) and \(n=41\). Hence, 218 is the 41st term. The 40th term is \(212\), so it is a close but incorrect option. Exam tip: When two terms are given, first find \(d\) using the difference in 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.
