If the (5)th term of an AP is (x+7) and the (12)th term is (x+42), what is the (20)th term in terms of (x)?
Answer and explanation
Correct answer: \(x+82\)
There are 7 positions between the 5th and 12th terms. Thus, \(a_{12}-a_5=7d\), so \((x+42)-(x+7)=35=7d\), giving \(d=5\). From the 12th term to the 20th term, there are 8 positions; hence \(a_{20}=a_{12}+8d=x+42+8(5)=x+82\). The option \(x+77\) results from incorrectly using a gap of only 7 positions. Exam tip: the difference between term numbers gives the multiplier of \(d\).
Frequently asked questions
What is the correct answer to this question?
\(x+82\)
Why is this the correct answer?
There are 7 positions between the 5th and 12th terms. Thus, \(a_{12}-a_5=7d\), so \((x+42)-(x+7)=35=7d\), giving \(d=5\). From the 12th term to the 20th term, there are 8 positions; hence \(a_{20}=a_{12}+8d=x+42+8(5)=x+82\). The option \(x+77\) results from incorrectly using a gap of only 7 positions. Exam tip: the difference between term numbers gives the multiplier of \(d\).
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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