SOLUTION: The third term of an arithmetic sequence is -12 and the seventb term is 8. What is the the sum of the first 10 terms? Please show me your solution. Thanks! Godbless -Student

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Question 1039756: The third term of an arithmetic sequence is -12 and the seventb term is 8. What is the the sum of the first 10 terms? Please show me your solution. Thanks! Godbless
-Student
Found 2 solutions by Fombitz, Edwin McCravy:
Answer by Fombitz(32388)   (Show Source): You can put this solution on YOUR website!

1.
.
.

2.
Subtract 1 from 2,



and



So then,



So,
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!


      ,       ,   -12 ,       ,       ,       ,    8  , ...

Let d be the common difference between terms, then
we subtract d each time going to the left of -12, and
we add d each time going to the right of -12.

-12-2d,  -12-d,   -12 , -12+d , -12+2d, -12+3d, -12+4d, ...

So -12+4d = 8 
       4d = 20
        d = 5

Then first term = a1 = -12-2d = -12-2(5) = -12-10 = -22









 



  -22 ,   -17 ,   -12 ,   -7  ,   -2  ,    3  ,    8  ,    13 ,    18 ,   23  , ...

Checking: -22-17-12-7-2+3+8+13+18+23 = 5

Edwin
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