In an AP, (a_8=27) and (a_{18}=77). Which term will be (152)?
Answer and explanation
Correct answer: 33rd term
Given \(a_8=27\) and \(a_{18}=77\), the common difference is \(d=\frac{77-27}{18-8}=5\). Using \(a_n=a_8+(n-8)d\), we get \(152=27+(n-8)\times5\). Thus, \(125=5(n-8)\), so \(n-8=25\) and \(n=33\). Hence, 152 is the 33rd term. The 32nd term would be \(147\), so it is not correct. 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?
33rd term
Why is this the correct answer?
Given \(a_8=27\) and \(a_{18}=77\), the common difference is \(d=\frac{77-27}{18-8}=5\). Using \(a_n=a_8+(n-8)d\), we get \(152=27+(n-8)\times5\). Thus, \(125=5(n-8)\), so \(n-8=25\) and \(n=33\). Hence, 152 is the 33rd term. The 32nd term would be \(147\), so it is not correct. 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.
