Question 1171297: Find the sum of the first 21 terms of the progression -10, -8, -6, .....
Answer by greenestamps(13200)   (Show Source):
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The average of any set of numbers is the sum of the numbers, divided by how many numbers there are.
Therefore, the sum of any set of number is the number of numbers, multiplied by the average of the numbers.
In an arithmetic progression like this, because the numbers are evenly spaced, the average of all the numbers is the average of the first and last numbers.
So the sum of n terms of an arithmetic sequence with first term a(1) and n-th term a(n) is
(number of numbers) times (average of first and last)
Algebraically, that is
But don't just memorize the formula -- understand what it means and why it gives you the sum.
You are given the first few terms of the progression, so you know the first term; and you are given the number of terms in the progression. So to find the sum you only need to determine the last (21st) number and do some simple calculations.
(1) Use the given information to determine the 21st term
(2) Find the average of the first and last terms
(3) Multiply that average by the number of terms (21) to get the desired sum
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