SOLUTION: Find the sum. 5+10+15+...+430 a.) 18,275 b.) 18,705 c.) 37845/2 d.) 18,490

Algebra ->  Sequences-and-series -> SOLUTION: Find the sum. 5+10+15+...+430 a.) 18,275 b.) 18,705 c.) 37845/2 d.) 18,490      Log On


   

Question 1059609: Find the sum. 5+10+15+...+430
a.) 18,275
b.) 18,705
c.) 37845/2
d.) 18,490
Found 2 solutions by ikleyn, Edwin McCravy:
Answer by ikleyn(52790) About Me  (Show Source):
You can put this solution on YOUR website!
.
Solved in
https://www.algebra.com/algebra/homework/Sequences-and-series/Sequences-and-series.faq.question.1059610.html

https://www.algebra.com/algebra/homework/Sequences-and-series/Sequences-and-series.faq.question.1059610.html


Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!

5+10+15+...+430

Factor out 5

5(1+2+3+...+86)

Now we know there are 86 numbers being added up.

Let's find the sum of 1+2+3+...+86
Call it S:

 S =  1+ 2 +3+ 4+...+82+83+84+85+86
 S = 86+85+84+83+...+ 5+ 4+ 3+ 2+ 1  <-- turn them backwards 
-----------------------------------
2S = 87+87+87+87+...+87+87+87+87+87  <-- adding the two equations
 S = 86*87
 S = 7482
 S = 3741

So 5+10+15+...+430 = 5(1+2+3+...+86) = 5(3741) = 18705

Edwin