If the (8)th term of an AP is (x+19) and the (20)th term is (x+91), what is the (35)th term in terms of (x)?
Answer and explanation
Correct answer: \(x+181\)
There are 12 term-intervals between the 8th and the 20th terms. Hence, \(12d=(x+91)-(x+19)=72\), so \(d=6\). From the 20th term to the 35th term, there are 15 intervals; therefore, \(a_{35}=x+91+15\times6=x+181\). Thus, \(x+181\) is correct. \(x+175\) would result from incorrectly using only 14 intervals. Exam tip: first find \(d\) from the two given terms, then count the term-intervals from the nearer known term.
Frequently asked questions
What is the correct answer to this question?
\(x+181\)
Why is this the correct answer?
There are 12 term-intervals between the 8th and the 20th terms. Hence, \(12d=(x+91)-(x+19)=72\), so \(d=6\). From the 20th term to the 35th term, there are 15 intervals; therefore, \(a_{35}=x+91+15\times6=x+181\). Thus, \(x+181\) is correct. \(x+175\) would result from incorrectly using only 14 intervals. Exam tip: first find \(d\) from the two given terms, then count the term-intervals from the nearer known term.
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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