If an arithmetic progression has (a_4=23) and (a_{13}=77), what is (d)?
Answer and explanation
Correct answer: 6
In an arithmetic progression, the difference between two terms equals the difference in their positions multiplied by the common difference. Thus, \(a_{13}-a_4=(13-4)d\), so \(77-23=9d\). Hence, \(54=9d\) and \(d=6\). If 5 were used, the difference across 9 positions would be 45, not the given difference of 54. Exam tip: subtract the term positions carefully as well as the terms.
Frequently asked questions
What is the correct answer to this question?
6
Why is this the correct answer?
In an arithmetic progression, the difference between two terms equals the difference in their positions multiplied by the common difference. Thus, \(a_{13}-a_4=(13-4)d\), so \(77-23=9d\). Hence, \(54=9d\) and \(d=6\). If 5 were used, the difference across 9 positions would be 45, not the given difference of 54. Exam tip: subtract the term positions carefully as well as the terms.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Arithmetic Progression.
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