What is a 'shortcut' for finding the sum of terms in a sequence

For example, this could be my sequence:
11, 15, 19, 23, 27, 31, 35, and so on
How would I find the sum of those terms without taking the time to add them all one by one. Is there a formula I can use?

Well, the sequence given seems to be on the form a(n) = a(n-1) + 4, or a(n) = 11 + 4k, where k is the term in the sequence (starting from 0 and going upwards, 1, 2, 3, and so on).

So in this case, it's quite simple. If you want the sum up to, say, the fifth term (11, 15, 19, 23, 27) you can take the first term and the last term, add them together (11 + 27 = 38), multiply by the number of terms (38 * 5 = 190) and divide by 2 (giving 95). Checking, this seems to fit - 11 + 15 + 19 + 23 + 27 = 95.

===use the average===
if it's linear like you have then take the average:
average = (lowest + highest) / 2

then if you have n terms, get the total:
total = average * n



===example {11, 15, 19, 23, 27, 31, 35}:===
average
= (11 + 35) / 2
= 23

total
= 23 * 7
= 161

Well if you know that you're dealing with a linear sequence, you can...

take the highest, minus the lowest.

35-11=24

and divide it by the number of elements (n) minus one.

24/(7-1)=4

x=11+4(n-1)