What is the difference between the sums of the first (225) and first (175) natural numbers?
Answer and explanation
Correct answer: 10025
The sum of the first n natural numbers is
\(S_n=\frac{n(n+1)}{2}\). Thus,
\(S_{225}=\frac{225\times226}{2}=25425\) and
\(S_{175}=\frac{175\times176}{2}=15400\). Therefore, the difference is
\(25425-15400=10025\). It is also the sum of the integers from 176 to 225. Exam tip: the difference of two such sums equals the sum of the remaining consecutive terms.
Frequently asked questions
What is the correct answer to this question?
10025
Why is this the correct answer?
The sum of the first n natural numbers is
\(S_n=\frac{n(n+1)}{2}\). Thus,
\(S_{225}=\frac{225\times226}{2}=25425\) and
\(S_{175}=\frac{175\times176}{2}=15400\). Therefore, the difference is
\(25425-15400=10025\). It is also the sum of the integers from 176 to 225. Exam tip: the difference of two such sums equals the sum of the remaining consecutive terms.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Sum of first n natural numbers.
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