What is the sum of the first (20) terms of the arithmetic progression (3,7,11,15,\ldots)?
Answer and explanation
Correct answer: 820
Here, the first term is \(a=3\), the common difference is \(d=7-3=4\), and \(n=20\). Using \(S_n=\frac{n}{2}[2a+(n-1)d]\), \(S_{20}=\frac{20}{2}[2(3)+19(4)]=10(82)=820\). Therefore, 820 is correct. A value such as 810 can result from using an incorrect last term or replacing \((n-1)d\) incorrectly. Exam tip: for the sum of \(n\) terms, use \((n-1)d\) in the formula.
Frequently asked questions
What is the correct answer to this question?
820
Why is this the correct answer?
Here, the first term is \(a=3\), the common difference is \(d=7-3=4\), and \(n=20\). Using \(S_n=\frac{n}{2}[2a+(n-1)d]\), \(S_{20}=\frac{20}{2}[2(3)+19(4)]=10(82)=820\). Therefore, 820 is correct. A value such as 810 can result from using an incorrect last term or replacing \((n-1)d\) incorrectly. Exam tip: for the sum of \(n\) terms, use \((n-1)d\) in the formula.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Arithmetic Progression.
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