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The third term of an arithmetic sequence is 9 and the seventh term is 31. Find the sum of the first twenty-two terms.
___, ___, 9 , ___, ___, ___, 31, ...
The nth term formula is
Now Substitute in
So we have the system:
Solve the first equation for
Substitute in the second equation:
Now we can use the formula for the sum of the
first n terms:
Substitute , ,
How many terms of the arithmetic sequence 2,4,6,8, ... add up to 60,762
Subtract any two consecutive terms and get
= the first term, which is , and
Multiply both sides by 2:
Divide through by 2
We discard the negative answer, and so