SOLUTION: 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 t

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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 , , 








----------------

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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