Question

If the sum of 5 consecutive positive integers is w, in terms of w, what represents the sum of the next 5 consecutive positive integers?

Answer 1

Ok, assume the original 5 numbers were x, x+1, ..., x+4. The next 5 numbers are x+5, x+6, ..., x+9. That's 25 more than the original sum, I believe.

Answer 2

But what i don't get is that w represents the whole sum, so why would it begin with x, x+1...x+4 ?

Answer 3

I just picked a name for the first of the 5 consecutive positive integers. That just makes it easier to write the original equation.

w=x + (x+1) + (x + 2) + (x + 3) + (x + 4)
Now let's call z the sum of the next 5:
z=(x+5)+(x+6)+(x+7)+(x+8)+(x+9)

But now compare the terms. x+5 compared to x is 5 more. x+6 compared to x+1 is 5 more. In fact, each term is 5 greater than the corresponding term in the first equation. So z is 25 greater than w.

Answer 4

Ooh! kk thank you :)

Answer 5

Let n be the middle number of five consecutive numbers. The sum of the five consecutive numbers is:
n - 2 + n - 1 + n + n + 1 + n + 2 = 5n
w=5n
The sum of the next consecutive five numbers is:
5 ( n + 5 ) = 5 n + 25 = w +25

Answer 6

Thank you for the medals