What is the sum of the finite arithmetic series?

(–10) + 0 + 10 + 20 + … + 130

Question

What is the sum of the finite arithmetic series?

(–10) + 0 + 10 + 20 + … + 130

tkhunny · Answer

You should have a formula for that.  Without such a formula, is your algebra up tp speed so you can CREATE it?

-10 = -10 + 0
0 = -10 + 10
10 = -10 + 2*10
20 = -10 + 3*10
...
130 = -10 + 14*10

That's 15 terms, so

-10*15 + 10(0 + 1 + 2 + 3 + ... + 14) = -10*15 + 10(15*7) = 10*15*(-1 + 7)

Did we get anywhere?

anonymous · Answer

Sum of {-10+(10*k)} from k=0 to infinity.

anonymous · Answer

Do you mean this formula, I just learned it

$$\large s_n = \dfrac{n(a_1+a_n)}{2}$$

$$\large s_{15} = \dfrac{15(-10+130)}{2}$$

$$\large s_{15} = \dfrac{15(-10+130)}{2}$$
$$\large s_{15} = 900$$

anonymous · Answer

Formula is

{C+dK} from K=0 to infinity

C = first term. -10
d = 10
K = sequence #

tkhunny · Answer

Will you look at that?!  6*10*15 = 900.  Almost magic!

anonymous · Answer

Was that correct?
Please medal if it was correct.

tkhunny · Answer

@1Rascal Good try, but an infinite arithmetic series with a difference of 10 will not be adding up to anything anytime soon.