If an arithmetic progression has (a_6=38) and (a_{14}=94), what is (d)?
Answer and explanation
Correct answer: \(7\)
For an arithmetic progression, \(a_n=a+(n-1)d\). Therefore, \(a_{14}-a_6=(14-6)d=8d\). Using the given values, \(94-38=56=8d\), so \(d=7\). If \(d=6\), the difference across 8 positions would be only \(48\), not the required \(56\). Exam tip: when two terms are given, divide the difference of their values by the difference of their term numbers.
Frequently asked questions
What is the correct answer to this question?
\(7\)
Why is this the correct answer?
For an arithmetic progression, \(a_n=a+(n-1)d\). Therefore, \(a_{14}-a_6=(14-6)d=8d\). Using the given values, \(94-38=56=8d\), so \(d=7\). If \(d=6\), the difference across 8 positions would be only \(48\), not the required \(56\). Exam tip: when two terms are given, divide the difference of their values by the difference of their term numbers.
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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