The sum of an arithmetic series is n times the average of the first and last terms. 1 + 2 + … + 10 is 10 times 5.5, which is 55. Sequences as a set are in sequences.
Count n, then average the ends
If the first term is 3, the last is 27, and the common difference is 4, n = ((27 − 3) / 4) + 1 = 7. Sum = 7 times (3 + 27) / 2 = 105. Combinations are a different counting tool, in the combinations formula.
The short list is in ACT Math formulas. Mean as an average of a list is in mean, median, and mode.
The bottom line
Sum = n(first + last) / 2. Count n before you multiply.
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