We solve various types of word problems comprehensively.
📘 Example ①
When the sum of the integers from 1 to n is 45, find n.
Answer:n(n+1)/2 = 45 → n² + n − 90 = 0 → (n+10)(n−9) = 0 → n = 9
When the sum of the integers from 1 to n is 45, find n.
Answer:n(n+1)/2 = 45 → n² + n − 90 = 0 → (n+10)(n−9) = 0 → n = 9
💡 Key Point
- Use the sum from 1 to n = n(n+1)/2
- Check the conditions, such as being a natural number, and select the solution
Practice Problems
- When the product of two consecutive odd numbers is 143, find the two numbers.
Answers and Explanations
- Answer:11 and 13。Let the smaller number be x: x(x+2)=143 → x²+2x−143=0 → (x+13)(x−11)=0 → x=11。