[igotrhythm]

Another way to look at it is to write out the first few and last few terms of the series. This also might give you some insight into how that summation formula came about.

K starts at 10. 7K-2 then equals 68. When K=11, 7K-2=75. And so on, up to K=70 when 7K-2=488.

The sigma is really just a short way of expressing
68+75+82+...+474+481+488. Let's see what happens when we add that series to itself...but the second one is turned around!
488+481+474+...+82+75+68. This is the same as the first because addition is commutative. Now we add up pairs of terms.

68+488=556
75+481=556
82+474=556

Hey, there's a pattern! Each pair adds up to the same number! And since we know how many pairs there are, we can just multiply that out! 556*61=33916...but wait, that's the result of TWICE the sum. So after we've divided by 2, we find that the sum is 16958.

So yeah, you're reading it wrong. A summation equals half of the number of terms in the series, times the sum of the first and last terms. The formula you were trying to use at first only works when the number of terms equals the value of n.

(this is what I get for trying to be fancy)