What is the sum of the first (15) terms of the arithmetic progression (14,22,30,\ldots)?
Answer and explanation
Correct answer: 1050
Here, the first term is \(a=14\), the common difference is \(d=22-14=8\), and \(n=15\). Using \(S_n=\frac{n}{2}[2a+(n-1)d]\), \(S_{15}=\frac{15}{2}[2(14)+14(8)]=\frac{15}{2}(140)=1050\). Hence, 1050 is correct. A value such as 1040 usually results from an addition or multiplication error. Exam tip: calculate \(n-1\) first before substituting in the formula.
Frequently asked questions
What is the correct answer to this question?
1050
Why is this the correct answer?
Here, the first term is \(a=14\), the common difference is \(d=22-14=8\), and \(n=15\). Using \(S_n=\frac{n}{2}[2a+(n-1)d]\), \(S_{15}=\frac{15}{2}[2(14)+14(8)]=\frac{15}{2}(140)=1050\). Hence, 1050 is correct. A value such as 1040 usually results from an addition or multiplication error. Exam tip: calculate \(n-1\) first before substituting 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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