SOLUTION: An arithmetic series has a third term of 0. The sum of the first 15 terms is � 300. What is the first term?

Question 692570: An arithmetic series has a third term of 0. The sum of the first 15 terms is � 300. What is the first term?
Found 2 solutions by mouk, MathTherapy:
Answer by mouk(232) (Show Source): You can put this solution on YOUR website!
1st term = a, common difference = d
So terms are, a, a+d, a+2d, ...
3rd term = 0 means that ............ Eq (1)
so
and

............ Eq (2)
Eq (2) - 7 Eq (1) gives:

, which is the first term

NB, If you need d then Eq (2) - 2 Eq (1) gives:

Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!

An arithmetic series has a third term of 0. The sum of the first 15 terms is � 300. What is the first term?

Formula for d, or the common difference in a series: , with = = 0, and n = 3

Therefore, becomes: ------ ------ eq (i)

Formula for sum of a series of numbers, or : , with = = - 300 ; and n = 15

Therefore, becomes: --- --- --- eq (ii)

------ Substituting for d in eq (ii)

, or 1st term = , or

You can do the check!!

Send comments and �thank-yous� to �D� at MathMadEzy@aol.com
RELATED QUESTIONS
An arithmetic series has a sum of -823.5 with 27 terms. The first term is 5. Determine... (answered by ikleyn,greenestamps)
Determine the sum of the first 15 terms of an arithmetic series if the middle term is... (answered by rothauserc)
What is the common difference? An arithmetic series has 9 terms with a sum of -135. It... (answered by ikleyn,MathTherapy,greenestamps)
The first three terms of an arithmetic series have a sum of 24 and a product of 312. What (answered by Edwin McCravy)
The sum of the first 12 terms of an arithmetic series is 186, and the 20th term is 83.... (answered by Edwin McCravy)
The sum of the first 25 terms of an arithmetic series with a common difference of 5 is... (answered by stanbon)
the sum of the first twenty-one terms of an arithmetic series is 273. The fifth term is... (answered by scott8148)
An arithmetic series has 20 terms. The first is -50 and the last term is 83, find the sum (answered by checkley77)
In Arithmetic series, the 3rd term is twice the 8th term. Find the sum of the first 25... (answered by rothauserc)