the sum of the integers from 1 to 10, inclusive, is 55. What is the sum of the multiples of 5 from 5 to 50 inclusive?

Which equation would I use?

To find the sum of the multiples of 5 from 5 to 50 inclusive, you would use the equation for the sum of an arithmetic series.

The formula for the sum of an arithmetic series is:

S = (n/2)(a + l)

where S represents the sum, n represents the number of terms, a represents the first term, and l represents the last term of the series.

In this case, the first term (a) is 5, the last term (l) is 50, and we need to find the number of terms (n).

To find the number of terms, we can use the formula:

n = (l - a) / d + 1

where d represents the common difference. In this case, the common difference is 5, since we are finding the multiples of 5.

Substituting the values into the formula:

n = (50 - 5) / 5 + 1
n = 45 / 5 + 1
n = 9 + 1
n = 10

According to the formula, there are 10 terms in the series.

Now, we can substitute the values into the formula for the sum:

S = (n/2)(a + l)
S = (10/2)(5 + 50)
S = 5(55)
S = 275

Therefore, the sum of the multiples of 5 from 5 to 50 inclusive is 275.

Wait is the answer 275? First i use the term equation to find 10 terms then I use the sum equation to find the sum right?

Yes, you are adding

5+10+15+...+45+50
here a=5 and d = 5
How many terms are there?
term(n) = a+(n-1)d
50 = 5 + (n-1)(5)
45 = 5n - 5
50 = 5n
n = 10

so we want the sum of 10 terms
sum = (10/2)(first + last)
= 5(5+ 50) = 275

or, you can think of it as

5+10+...+50 = 5(1+2+...+10) = 5*55 = 275

I like Steve's thinking, but sometimes I like to take a hammer to a thumbtack.