SOLUTION: How many terms ofthe sequence -24, -15, -6, and 3 will give a sum of 1230?

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Question 1041613: How many terms ofthe sequence -24, -15, -6, and 3 will give a sum of 1230?

Found 3 solutions by Fombitz, ikleyn, MathTherapy:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
a%5B1%5D=-24
a%5Bn%5D=3
S%5Bn%5D=1230
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On the face of it, you're adding a bunch of negative numbers (if the difference between the two numbers is 9, then 3 is the only positive number) to get a large positive sum.
Something is wrong with your problem setup.
Please check it and repost with a corrected question.

Answer by ikleyn(52790) About Me  (Show Source):
You can put this solution on YOUR website!
.
How many terms of the sequence -24, -15, -6, and 3 will give a sum of 1230?
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It is an arithmetic progression, first term is -24, the common difference is 9. 


The sum of the first n terms is equal to

S%5Bn%5D = %28a%5B1%5D+%2B+%28%28n-1%29%2Ad%29%2F2%29%2An

(see the lesson Arithmetic progressions in this site).  Or

1230 = %28-24+%2B+%28%28n-1%29%2A9%29%2F2%29%2An.

Solve this equation for n and get the answer.


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

How many terms ofthe sequence -24, -15, -6, and 3 will give a sum of 1230?
Use the formula for the SUM of an AP: S%5Bn%5D+=+%28n%2F2%29%282a%5B1%5D+%2B+%28n+-+1%29d%29, where:
a%5B1%5D = First term in AP (- 24 in this case)
S%5Bn%5D = Sum of n terms (1,230 in this case)
n = number of terms in the AP (unknown)
d = Common difference (9 in this case)
Thus, S%5Bn%5D+=+%28n%2F2%29%282a%5B1%5D+%2B+%28n+-+1%29d%29 becomes: S%5Bn%5D+=+%28n%2F2%29%282%28-+24%29+%2B+%28n+-+1%299%29
matrix%281%2C1%2C+%221%2C230%22%29+=+%28n%2F2%29%28-+48+%2B+9n+-+9%29
Continue to solve for n (the number of terms). You should get highlight_green%28matrix%281%2C2%2C+20%2C+terms%29%29