In an AP, (a_{11}=4a_3) and (a_3=18). What is (a_{15})?
Answer and explanation
Correct answer: 99
Given \(a_3=18\), we get \(a_{11}=4a_3=4\times18=72\). In an AP, \(a_{11}-a_3=(11-3)d=8d\). Thus, \(8d=72-18=54\), so \(d=\frac{27}{4}\). Now \(a_{15}=a_{11}+4d=72+4\times\frac{27}{4}=99\). Hence, 99 is correct. The value 96 would result from not accounting correctly for the common difference between the terms. Exam tip: use the difference in term numbers to find \(d\) when two terms are given.
Frequently asked questions
What is the correct answer to this question?
99
Why is this the correct answer?
Given \(a_3=18\), we get \(a_{11}=4a_3=4\times18=72\). In an AP, \(a_{11}-a_3=(11-3)d=8d\). Thus, \(8d=72-18=54\), so \(d=\frac{27}{4}\). Now \(a_{15}=a_{11}+4d=72+4\times\frac{27}{4}=99\). Hence, 99 is correct. The value 96 would result from not accounting correctly for the common difference between the terms. Exam tip: use the difference in term numbers to find \(d\) when two terms are given.
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.
