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

Algebra ->  Sequences-and-series -> 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      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
a%5B3%5D=a%5B0%5D%2B%283-1%29%2Ad=-12
1.a%5B0%5D%2B2d=-12
.
.
a%5B7%5D=a%5B0%5D%2B%287-1%29%2Ad=8
2.a%5B0%5D%2B6d=8
Subtract 1 from 2,
a%5B0%5D%2B6d-a%5B0%5D-2d=8-%28-12%29
4d=20
d=5
and
a%5B0%5D%2B6%285%29=8
a%5B0%5D=8-30
a%5B0%5D=-22
So then,
a%5B10%5D=-22%2B%2810-1%295
a%5B10%5D=-22%2B45
a%5B10%5D=23
So,
S%5B10%5D=%2810%2F2%29%28-22%2B23%29
S%5B10%5D=5

Answer by Edwin McCravy(20056) About Me  (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

S%5Bn%5D%22%22=%22%22expr%28n%2F2%29%282a%5B1%5D%2B%28n-1%29d%5E%22%22%29

S%5B10%5D%22%22=%22%22expr%2810%2F2%29%282%28-22%29%2B%2810-1%29%285%29%5E%22%22%29

S%5B10%5D%22%22=%22%225%28-44%2B%289%29%285%29%5E%22%22%29

S%5B10%5D%22%22=%22%225%28-44%2B45%5E%22%22%29

S%5B10%5D%22%22=%22%225%281%5E%22%22%29 

S%5B10%5D%22%22=%22%225

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

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

Edwin