If \(S_n=\frac{n}{2}(a+l)\), \(a=25\), \(l=5\), and \(n=7\), what is the sum?
Answer and explanation
Correct answer: 105
The sum of the first \(n\) terms of an AP is \(S_n=\frac{n}{2}(a+l)\). Substituting the given values, \(S_7=\frac{7}{2}(25+5)=\frac{7}{2}\times30=105\). Therefore, the correct answer is 105. Option 110 is incorrect because \(\frac{7}{2}\) times 30 equals 105, not 110. Exam tip: first add the values inside the brackets, then simplify with 2 before multiplying whenever possible.
Frequently asked questions
What is the correct answer to this question?
105
Why is this the correct answer?
The sum of the first \(n\) terms of an AP is \(S_n=\frac{n}{2}(a+l)\). Substituting the given values, \(S_7=\frac{7}{2}(25+5)=\frac{7}{2}\times30=105\). Therefore, the correct answer is 105. Option 110 is incorrect because \(\frac{7}{2}\) times 30 equals 105, not 110. Exam tip: first add the values inside the brackets, then simplify with 2 before multiplying whenever possible.
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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