The sum of the first (7) terms of an arithmetic progression is (203). If the first term is (5), what is the seventh term?
Answer and explanation
Correct answer: 53
For an AP, \(S_n=\frac{n}{2}(a+l)\), where \(l\) is the last term. Thus, \(203=\frac{7}{2}(5+l)\). So \(406=7(5+l)\), giving \(5+l=58\) and hence \(l=53\). Option 58 is the value of \(a+l\), not the seventh term. Exam tip: When the sum and the last term are involved, use \(S_n=\frac{n}{2}(a+l)\).
Frequently asked questions
What is the correct answer to this question?
53
Why is this the correct answer?
For an AP, \(S_n=\frac{n}{2}(a+l)\), where \(l\) is the last term. Thus, \(203=\frac{7}{2}(5+l)\). So \(406=7(5+l)\), giving \(5+l=58\) and hence \(l=53\). Option 58 is the value of \(a+l\), not the seventh term. Exam tip: When the sum and the last term are involved, use \(S_n=\frac{n}{2}(a+l)\).
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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