In an AP, (a_5+a_{11}=138) and (a_{18}=165). What is (a_{36})?
Answer and explanation
Correct answer: 337.8
For an AP, \(a_n=a+(n-1)d\). Hence, \(a_5+a_{11}=2a+14d=138\), so \(a+7d=69\). Also, \(a_{18}=a+17d=165\). Subtracting these equations gives \(10d=96\), so \(d=9.6\) and \(a=1.8\). Therefore, \(a_{36}=a+35d=1.8+35(9.6)=337.8\). Option 327 is incorrect because it does not follow from the common difference determined by the given conditions. Exam tip: Form equations from the given terms or sums of terms and subtract them to find \(d\) quickly.
Frequently asked questions
What is the correct answer to this question?
337.8
Why is this the correct answer?
For an AP, \(a_n=a+(n-1)d\). Hence, \(a_5+a_{11}=2a+14d=138\), so \(a+7d=69\). Also, \(a_{18}=a+17d=165\). Subtracting these equations gives \(10d=96\), so \(d=9.6\) and \(a=1.8\). Therefore, \(a_{36}=a+35d=1.8+35(9.6)=337.8\). Option 327 is incorrect because it does not follow from the common difference determined by the given conditions. Exam tip: Form equations from the given terms or sums of terms and subtract them to find \(d\) quickly.
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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