Please help which sigma notation is equivalent to the following series (check picture)

C

Step-by-step explanation:

Okay so what we are going to do here is look at our terms first and see what gets us there.

So lets consider the first term or the first sum, when k=1.

So if k=1 then the expression should give us a positive 5. So lets check each one for a +5.

So lets start with (5k-5) if we let k equal one this first term would be 0. So this doesnt work already.

The rest however do work so we need to keep checking.

Lets let k=2

We know that when k=2 we need the value of the term to equal -5.

So lets look at (-5k+10) if we let k be -5 then this second term would be 0 and 0 is not equal to -5 so this is now out.

Now lets look at (15k-10) if we let k=2 then this is (30-10) = 20 and 20 doesnt equal 5 so that not gonna work.

So our answer here must be (-10k+15). If we let k=2 then thats (-20+15) = -5

Now just to be 100% sure lets check some other terms. Lets check the last term which would be -755. This term would be the the 77th term so lets let k=77.

(-10(77) + 15) = -770 + 15 = -755. So that also works.

Hence our answer is the series/answer choice c.