Can someone check my answer on this series question?

Question

itiaax · Answer

So I was supposed to find the sum of the numbers from 1 to 200 that are multiples of 5 and the sum I ended up with was 4,100. Is this correct?

anonymous · Answer

i think so. thats hard

asnaseer · Answer

How did you arrive at that answer?

anonymous · Answer

youll add up 5, 10, 15, 20, 25, 30, 35, 40.... all the way to 200.

itiaax · Answer

No, I used the formula. Here is my working:
l=a+(n-1)d
Where l is the last term, a is the first term and d is the common difference.
200=5+5(n-1)
200=5+5n-5
n=200/5=40
S(40) = 40/2[5+200]
= 20(205)
=4,100

asnaseer · Answer

that is indeed correct - I just wanted to make sure you were not just guessing at the answer :)

A slightly simpler way to do this would be as follows:

5 + 10 + ... + 200 = 5(1 + 2 + ... + 40)

Then use the alternate formula for the sum of an arithmetic series:$$S=\frac{n}{2}(a+l)$$where "n" is the number of terms, "a" is the first term and "l" is the last term.

This gives:$$S=1+2+...+40=\frac{40}{2}(1+40)=20*41=820$$Therefore your sum$=5*820=4100$

itiaax · Answer

Wow, thank you for this alternative approach :)

asnaseer · Answer

yw :)