SOLUTION: write an explicit formula for the sequence 7, 2, -3, -8, -13,... then find a_14 http://prntscr.com/sob4im

Algebra ->  Sequences-and-series -> SOLUTION: write an explicit formula for the sequence 7, 2, -3, -8, -13,... then find a_14 http://prntscr.com/sob4im      Log On


   

Question 1160027: write an explicit formula for the sequence 7, 2, -3, -8, -13,... then find a_14
http://prntscr.com/sob4im
Found 3 solutions by ikleyn, MathLover1, josgarithmetic:
Answer by ikleyn(52794) About Me  (Show Source):
You can put this solution on YOUR website!
.

There are MANY (more than one) solutions to this request, giving different values for a_14.

Please STOP posting nonsense to this forum . . .


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comment from student: Thank you again for feedback that contributes nothing and is pointless!
You have not helped me once with questions I've posted that I've struggled with. :)
If you think me needing genuine help is nonsense, please STOP and keep your thoughts to yourself!
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My response : Why I should keep my thoughts to myself, while they are so correct and so beautiful ?

Is it true that you came to this forum to learn from tutors ?

Then learn from me, having this happy opportunity . . .

Or you, in opposite, came to teach me ? --- But I didn't ask you about it . . .


/\/\/\/\/\/\/\/

You really need help.  But this help is not in finding next number there,  where it is nonsensical.

The real help you need is to convince you that integer numbers  do not owe you anything.

If you think differently,  then collect at least one dollar from each natural number.

You will become a multi-billioner  (or even multi-trillioner)  then,  the manager over all natural numbers/dollars.


Then you will be able to assign  ANY  number to be next,  by the law,  issued by you,  yourself,  personally.


I wish you . . . (and so on . . . )

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In the short form, never come to this forum with such NONSENSICAL questions/ "problems".

And then everything will be Ok, in purple color.



Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

7, 2, -3,+-8,+-13
as you can see, if you subtract 5 from first term you get second term,
if you subtract 5 from second term you get third term, and so on
so, common difference is d=-5
general formula for nth term is:
a%5Bn%5D=a%5B1%5D%2Bd%28n-1%29...since a%5B1%5D=7 and d=-5
a%5Bn%5D=7-5%28n-1%29

check:
fourth term, n=4
a%5B4%5D=7-5%284-1%29
a%5B4%5D=7-5%283%29
a%5B4%5D=7-15
a%5B4%5D=-8-> true

now we can find a%5B14%5D where n=14
a%5B14%5D=7-5%2814-1%29
a%5B14%5D=7-5%2813%29
a%5B14%5D=7-65
a%5B14%5D=-58

Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
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7, 2, -3, -8, -13,... then find a_14
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Notice common difference to each successive term is 5, going downward for each. First term is 7.

Arithmetic Progression: General term 7%2B%28-5%29%28n-1%29 or 7-5%28n-1%29.


The fourteen term, n=14:
7-5%2814-1%29
7-5%2A13
highlight%28-58%29