SOLUTION: the 15th term in an arithmetic sequence is 43 and the sum of the first 15 terms of the series is 120. Determine the first three terms of the series
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Question 567832: the 15th term in an arithmetic sequence is 43 and the sum of the first 15 terms of the series is 120. Determine the first three terms of the series
Found 2 solutions by solver91311, issacodegard:
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
The sum of an arithmetic sequence is given by:
}{2})
Where 
is the number of terms, 
is the first term, 
is the last term, and 
is the sum of terms.
Plug in the given values of , , and and then solve for
Once you have the value for , you can use that to find 
, the common difference because the th term is given by:
d)
Plug in the values you know for 
, , and , then solve for .
Finally, calculate:
and
John
My calculator said it, I believe it, that settles it
Answer by issacodegard(60) (Show Source): You can put this solution on YOUR website!
Call the terms a_1,a_2,... then S_15=15*(a_1+a_15)/2=120. So, we solve for a_1,
a_1=-27. Then we need to know the common difference, d. We know that a_n=a_1+(n-1)d. So, d=(43-(-27))/14=5. So, a_2=a_1+d=-22, and a_3=a_2+d=-17.
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