If the (6)th term of an AP is (x+11) and the (15)th term is (x+65), what is the (27)th term in terms of (x)?
Answer and explanation
Correct answer: \(x+137\)
The difference between the 15th and 6th terms is \(9d\). Thus, \(9d=(x+65)-(x+11)=54\), so \(d=6\). From the 15th term to the 27th term, there are 12 common differences. Hence, \(a_{27}=x+65+12\times6=x+137\). Therefore, option B is correct. \(x+131\) would result from incorrectly using 11 common differences. Exam tip: Count the difference in term numbers carefully when moving between two AP terms.
Frequently asked questions
What is the correct answer to this question?
\(x+137\)
Why is this the correct answer?
The difference between the 15th and 6th terms is \(9d\). Thus, \(9d=(x+65)-(x+11)=54\), so \(d=6\). From the 15th term to the 27th term, there are 12 common differences. Hence, \(a_{27}=x+65+12\times6=x+137\). Therefore, option B is correct. \(x+131\) would result from incorrectly using 11 common differences. Exam tip: Count the difference in term numbers carefully when moving between two AP terms.
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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