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The houses in a row are numbered consecutively from 1 to 49. Show that there exist a value of x such that sum of number of houses proceeding the house numbered x is equal to the sum of the numbers of houses following x
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The houses in a row are numbered consecutively from 1 to 49. Show that...
Proof:
- Let's denote the house number x as the point where the sum of the numbers of houses before x is equal to the sum of the numbers of houses after x.
- The sum of the numbers of houses from 1 to 49 can be calculated using the formula for the sum of an arithmetic series: S = n/2 * (a + l), where S is the sum, n is the number of terms, a is the first term, and l is the last term.
- Substituting the values, we get S = 49/2 * (1 + 49) = 1225.
- Since the sum of the numbers of houses from 1 to x is equal to the sum of the numbers of houses from x+1 to 49, we have 2 * (1 + 2 + ... + x-1) + x = 1225 - x - (x+1) - ... - 49.
- Simplifying the equation, we get x = (1225 - 49*25) / 2 = 25.
- Therefore, the house numbered 25 is the point where the sum of the numbers of houses before it is equal to the sum of the numbers of houses after it.
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The houses in a row are numbered consecutively from 1 to 49. Show that...
can anyone give me the answer
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The houses in a row are numbered consecutively from 1 to 49. Show that there exist a value of x such that sum of number of houses proceeding the house numbered x is equal to the sum of the numbers of houses following x
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The houses in a row are numbered consecutively from 1 to 49. Show that there exist a value of x such that sum of number of houses proceeding the house numbered x is equal to the sum of the numbers of houses following x for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about The houses in a row are numbered consecutively from 1 to 49. Show that there exist a value of x such that sum of number of houses proceeding the house numbered x is equal to the sum of the numbers of houses following x covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The houses in a row are numbered consecutively from 1 to 49. Show that there exist a value of x such that sum of number of houses proceeding the house numbered x is equal to the sum of the numbers of houses following x.
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