If \(a_{20}=3a_8\) and \(a_8=28\), what is \(a_{26}\)?
Answer and explanation
Correct answer: 112
Given \(a_8=28\), \(a_{20}=3a_8=3\times28=84\). In an AP, \(a_{20}-a_8=(20-8)d=12d\). Hence, \(84-28=12d\), so \(d=\frac{14}{3}\). Now \(a_{26}=a_{20}+(26-20)d=84+6\times\frac{14}{3}=84+28=112\). Therefore, 112 is correct. Choosing 106 would mean adding the increase over six terms incorrectly. Exam tip: when two distant terms are given, use the difference of their indices to find \(d\).
Frequently asked questions
What is the correct answer to this question?
112
Why is this the correct answer?
Given \(a_8=28\), \(a_{20}=3a_8=3\times28=84\). In an AP, \(a_{20}-a_8=(20-8)d=12d\). Hence, \(84-28=12d\), so \(d=\frac{14}{3}\). Now \(a_{26}=a_{20}+(26-20)d=84+6\times\frac{14}{3}=84+28=112\). Therefore, 112 is correct. Choosing 106 would mean adding the increase over six terms incorrectly. Exam tip: when two distant terms are given, use the difference of their indices to find \(d\).
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.
