Question 202838: Algebra 2 worksheet on Arithmetic sequence
The third term of an arithmetic sequence is 9 and the seventh term is 31. Find the sum of the first twenty-two terms.
How many terms of the arithmetic sequence 2,4,6,8, ... add up to 60,762?
Answer by Edwin McCravy(20060)   (Show Source):
You can put this solution on YOUR website! 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
Substitute  in
Substitute 
Now Substitute  in
Substitute 
So we have the system:
Solve the first equation for 
Substitute  in the second equation:
Substituting  in
Now we can use the formula for the sum of the
first n terms:
Substitute  ,  ,
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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
Factor:
 or 
 or 
We discard the negative answer, and so
Edwin
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