SOLUTION: what is the a30 when a1=8000 and r=-1/2 I had gotten to here ---> 8000(-1/2^30-1) I am not getting a clear answer and am getting a very large decimal that does not seem to be

Question 892798: what is the a30 when a1=8000 and r=-1/2
I had gotten to here ---> 8000(-1/2^30-1)
I am not getting a clear answer and am getting a very large decimal that does not seem to be right.
answer gotten ---> -1.86264515E-9
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
A1 = 8000
An = A1 * r^(n-1)
r is equal to (-1/2).
n is equal to 30
A30 = 8000 * (-1/2)^(30-1) = 8000 * (-1/2)^29 = 8000 * -1.86264515 * 10^-9 which is equal to -1.49011612 * 10^-5.
that's a very small number.
pretty close to 0 but not quite.
it's in scientific notation.
converting that to decimal notation and the number becomes:
-.0000149011612.
the number is very reasonable if you consider that a ratio of (-1/2) means you are dividing 8000 by -2 for 28 times i believe.
here's the actual individual calculations using excel spreadsheet.
$$$

your -1.86264515E-9 is correct.
it means -1.86264515 * 10^-9
after you multiply that by 8000, you get -1.49011612 * 10^-5.
that's the value of A30.

the numbers are good.
maybe you didn't know they were in scientific format?
there are a lot of decimal places but the number is very small because the exponent part is -9 for the factor and -5 for the final answer which is the factor * 8000.

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