What is the sum of the first (20) terms of the arithmetic progression (1,4,7,10,\ldots)?
Answer and explanation
Correct answer: 590
Here, the first term is \(a=1\), the common difference is \(d=3\), and \(n=20\). The sum of the first \(n\) terms of an AP is \(S_n=\frac{n}{2}[2a+(n-1)d]\). Therefore, \(S_{20}=\frac{20}{2}[2(1)+19(3)]=10(59)=590\). Hence, 590 is correct. A result such as 600 may come from using an incorrect number of common differences. Exam tip: to reach the \(n\)th term from the first term, use \(n-1\) common differences.
Frequently asked questions
What is the correct answer to this question?
590
Why is this the correct answer?
Here, the first term is \(a=1\), the common difference is \(d=3\), and \(n=20\). The sum of the first \(n\) terms of an AP is \(S_n=\frac{n}{2}[2a+(n-1)d]\). Therefore, \(S_{20}=\frac{20}{2}[2(1)+19(3)]=10(59)=590\). Hence, 590 is correct. A result such as 600 may come from using an incorrect number of common differences. Exam tip: to reach the \(n\)th term from the first term, use \(n-1\) common differences.
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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