In an AP, (a_{4n}=140), (a_n=32), and (d=6). What is (n)?
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Answer and explanation
Correct answer: \(6\)
For an AP, \(a_{4n}-a_n=(4n-n)d=3nd\). Thus, \(140-32=3n\times6\), so \(108=18n\). Hence, \(n=6\). Note that the difference between the term indices is \(3n\), not \(4n\). Exam tip: When two terms are given, subtract their indices first and multiply the result by \(d\).
Frequently asked questions
What is the correct answer to this question?
\(6\)
Why is this the correct answer?
For an AP, \(a_{4n}-a_n=(4n-n)d=3nd\). Thus, \(140-32=3n\times6\), so \(108=18n\). Hence, \(n=6\). Note that the difference between the term indices is \(3n\), not \(4n\). Exam tip: When two terms are given, subtract their indices first and multiply the result by \(d\).
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.
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