If the (7)th term of an AP is (x+13) and the (18)th term is (x+90), what is the (32)nd term in terms of (x)?
Answer and explanation
Correct answer: \(x+188\)
For an AP, \(a_{18}-a_7=(18-7)d\). Thus, \((x+90)-(x+13)=11d\), so \(77=11d\) and \(d=7\). Now \(a_{32}=a_{18}+(32-18)d=x+90+14\times7=x+188\). Therefore, option B is correct. Choosing \(x+195\) would incorrectly use a gap of 15 terms, whereas the gap from the 18th to the 32nd term is 14. Exam tip: always subtract the term numbers to find the number of common differences between two terms.
Frequently asked questions
What is the correct answer to this question?
\(x+188\)
Why is this the correct answer?
For an AP, \(a_{18}-a_7=(18-7)d\). Thus, \((x+90)-(x+13)=11d\), so \(77=11d\) and \(d=7\). Now \(a_{32}=a_{18}+(32-18)d=x+90+14\times7=x+188\). Therefore, option B is correct. Choosing \(x+195\) would incorrectly use a gap of 15 terms, whereas the gap from the 18th to the 32nd term is 14. Exam tip: always subtract the term numbers to find the number of common differences between two 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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