SOLUTION: Could I please get help with the following problem: Find a general formula for the arithmetic sequence whose 8th term is -20 and the 17th term is -47 Thank You

Question 149625: Could I please get help with the following problem:
Find a general formula for the arithmetic sequence whose 8th term is -20 and the 17th term is -47
Thank You
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
If it is an "arithmetic sequence" there is a "constant difference" between each number in the series.
.
The formula for any number within that sequence is:
An = A1 + (n-1)d
where
An = value of the nth number within the series
A1 = first value of the sequence
n = nth term
.
In your problem they don't give you the difference (d) and you are asked to find that given all the other information.
.
Find a general formula for the arithmetic sequence whose 8th term is -20 and the 17th term is -47.
.
The distance is:
d = (-47-(-20))/(17-8)
d = (-47+20)/(17-8)
d = (-27)/(9)
d = -3
.
Now, plug in what we know into:
An = A1 + (n-1)d
An = -20 + (n-1)(-3)
An = -20 + (-3n+3)
An = -17 - 3n (this is what you're looking for)
.
For example, to find the 3rd number:
A(3) = -17 - 3(3)
A(3) = -17 - 9
A(3) = -26

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