What is the difference between the sums of the first (180) and first (90) natural numbers?
Answer and explanation
Correct answer: 12195
The sum of the first n natural numbers is \(S_n=\frac{n(n+1)}{2}\). Thus, \(S_{180}=\frac{180\times181}{2}=16290\) and \(S_{90}=\frac{90\times91}{2}=4095\). Hence, the difference is \(16290-4095=12195\). It is also the sum of the integers from 91 to 180; a value such as 12295 does not result from the formula or subtraction. Exam tip: write such a difference as \(S_{180}-S_{90}\).
Frequently asked questions
What is the correct answer to this question?
12195
Why is this the correct answer?
The sum of the first n natural numbers is \(S_n=\frac{n(n+1)}{2}\). Thus, \(S_{180}=\frac{180\times181}{2}=16290\) and \(S_{90}=\frac{90\times91}{2}=4095\). Hence, the difference is \(16290-4095=12195\). It is also the sum of the integers from 91 to 180; a value such as 12295 does not result from the formula or subtraction. Exam tip: write such a difference as \(S_{180}-S_{90}\).
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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