The (7)th term of an arithmetic progression is (34) and the (18)th term is (89). What is the sum of the first (18) terms?
Answer and explanation
Correct answer: 837
For an AP, \(a_7=a+6d=34\) and \(a_{18}=a+17d=89\). Subtracting the equations gives \(11d=55\), so \(d=5\). Then \(a+30=34\) gives \(a=4\). Hence, \(S_{18}=\frac{18}{2}[2a+17d]=9[8+85]=837\). An answer such as \(819\) can result from using an incorrect coefficient for the last term in the sum formula. Exam tip: when two terms are given, first write them as \(a+(n-1)d\) to find \(a\) and \(d\).
Frequently asked questions
What is the correct answer to this question?
837
Why is this the correct answer?
For an AP, \(a_7=a+6d=34\) and \(a_{18}=a+17d=89\). Subtracting the equations gives \(11d=55\), so \(d=5\). Then \(a+30=34\) gives \(a=4\). Hence, \(S_{18}=\frac{18}{2}[2a+17d]=9[8+85]=837\). An answer such as \(819\) can result from using an incorrect coefficient for the last term in the sum formula. Exam tip: when two terms are given, first write them as \(a+(n-1)d\) to find \(a\) and \(d\).
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Arithmetic Progressions (AP). Topic: Finding the sum of the first $n$ terms of an AP.
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