You can put this solution on YOUR website! MENTAL MATH (for multiple choice tests):
from one number to the next you are adding a common difference.
From the sixth term to the tenth term that common difference was added 4 times because .
That means that the common difference is .
In an AP, the 1st and 20th terms
add to the same sum as
the 2nd and 19th terms,
the 3rd and 18th terms, and so on until we get to
the 10th and 11th terms, in the middle of the first 20 terms.
The 10th term is as we were told,
and the 11th term is .
The sum of 20 first terms is made of the 10 sums listed above,
and each of those sums is .
So the sum of the first 20 terms is
That is a lot of words, but you can think through the concepts and calculations much faster than you can explain and write them.
USING FORMULAS (to please the teacher by "showing your work"): = first term = common difference = general formula for term number .
For we know that
For we know that is solved to get
Then we apply some formula for the sum of the first terms.
Maybe the formula you were given is (or some variation of that).
Or maybe you were given (or some variation of that).
With and
you would calculate the 20th term as
and then you would calculate the sum of the first 20 terms as
With you would calculate
