Summations Problem: Sum of Multiples of 5 from 5-1550

  • Thread starter elainehula
  • Start date
In summary, the sum of all whole numbers which are multiples of 5 from 5 to 1550 is 478950. This can be calculated by dividing 1550 by 5 to get the number of terms, which is 310. Then, the sum of an arithmetic progression can be used to find the total sum, which is equal to 5 times the sum of numbers from 1 to 310. The incorrect attempt at a solution was due to incorrect use of parentheses in the equation.
  • #1
elainehula
1
0

Homework Statement


Sum all the whole numbers which are multiples of 5 from 5 to 1550


Homework Equations





The Attempt at a Solution


1550÷5=310
1550-5x310= 478950
 
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  • #2
elainehula said:

Homework Statement


Sum all the whole numbers which are multiples of 5 from 5 to 1550


Homework Equations





The Attempt at a Solution


1550÷5=310
1550-5x310= 478950

Hint: Sum of arithmetic progression or, alternatively,$$
\sum_{k=1}^{310}5k = 5\sum_{k=1}^{310}k$$
 
  • #3
elainehula said:

Homework Statement


Sum all the whole numbers which are multiples of 5 from 5 to 1550


Homework Equations





The Attempt at a Solution


1550÷5=310
Yes, that is correct

1550-5x310= 478950
No, 1550- 5x 310= 0, That is what [tex]1550÷5= 310[/tex] means!
 
  • #4
HallsofIvy said:
Yes, that is correct


No, 1550- 5x 310= 0, That is what [tex]1550÷5= 310[/tex] means!

She is using the parentheses differently (incorrectly so , by priority of operations):

1550-5=1545 , 1545x310= 474950
 

1. What is the Summations Problem: Sum of Multiples of 5 from 5-1550?

The Summations Problem is a mathematical problem that asks for the sum of all the multiples of 5 within a given range, specifically from 5 to 1550.

2. How do you solve the Summations Problem: Sum of Multiples of 5 from 5-1550?

To solve this problem, you can use the formula for the sum of an arithmetic series: Sn = n/2 * (a1 + an), where n is the number of terms, a1 is the first term, and an is the last term. In this case, n = (1550-5)/5 + 1 = 310, a1 = 5, and an = 1550. Plugging these values into the formula, we get Sn = 310/2 * (5 + 1550) = 240,775.

3. What is the significance of the Summations Problem: Sum of Multiples of 5 from 5-1550?

The Summations Problem has practical applications in various fields, such as computer science, economics, and physics. It also helps students to practice their algebraic and arithmetic skills.

4. Can the Summations Problem: Sum of Multiples of 5 from 5-1550 be solved using a different approach?

Yes, there are several other methods to solve this problem, such as using a loop or recursion in programming, or manually adding the multiples of 5 within the given range.

5. Is there a general formula for finding the sum of multiples of a number within a given range?

Yes, the formula for the sum of multiples of a number within a range is Sn = n/2 * (a1 + an), where n is the number of terms, a1 is the first term, and an is the last term. This formula can be applied to any range and any multiple.

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