What is the ratio of the sums of the first (90) and first (60) natural numbers?
Answer and explanation
Correct answer: 273:122
The sum of the first n natural numbers is \(S_n=\frac{n(n+1)}{2}\). Thus, \(S_{90}=\frac{90\times91}{2}=4095\) and \(S_{60}=\frac{60\times61}{2}=1830\). Therefore, \(4095:1830=273:122\). The ratio \(3:2\) is only the ratio of 90 to 60, not of their sums. Exam tip: When comparing such sums, include the \(n+1\) factor in \(n(n+1)/2\).
Frequently asked questions
What is the correct answer to this question?
273:122
Why is this the correct answer?
The sum of the first n natural numbers is \(S_n=\frac{n(n+1)}{2}\). Thus, \(S_{90}=\frac{90\times91}{2}=4095\) and \(S_{60}=\frac{60\times61}{2}=1830\). Therefore, \(4095:1830=273:122\). The ratio \(3:2\) is only the ratio of 90 to 60, not of their sums. Exam tip: When comparing such sums, include the \(n+1\) factor in \(n(n+1)/2\).
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.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
