What is the sigma notation for this arithmetic series : 10+25+40 + ... + 490+505

Sum (from n = 0 to n = 33) of 10 + 15 * n

Step-by-step explanation:

The sigma notation is to express an arithmetic series as a summation, in this case we can see that it starts at 10 and ends at 505.

What we can notice is that the values are increasing by 15 units, therefore that will be the proportion that accompanies "n".

Now, we must calculate, how many times is "n", in the final value, for this we subtract the initial value, that is 10 and divide it by 15.

505 - 10 = 495/15 = 33

So "n" goes up to 33

So that series is expressed like this:

Sum (from n = 0 to n = 33) of 10 + 15 * n