SOLUTION: How do I find the general term of the arithmetic sequence a19= 150, d=9, without the first term?

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Question 1045441: How do I find the general term of the arithmetic
sequence a19= 150, d=9, without the first term?

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
How do I find the general term of the arithmetic
sequence a19 = 150, d=9, without the first term?
Solve for the first term:

a%5Bn%5D=a%5B1%5D%2B%28n-1%29d

Substitute n=19, d=9

a%5B19%5D=a%5B1%5D%2B%2819-1%299

a%5B19%5D=a%5B1%5D%2B%2818%299

a%5B19%5D=a%5B1%5D%2B162

Substitute 150 for a9

150=a%5B1%5D%2B162

Subtract 162 from both sides

-12=a%5B1%5D

So the nth term is

a%5Bn%5D=a%5B1%5D%2B%28n-1%29d

Substitute a1=-12 and d=9

a%5Bn%5D=-12%2B%28n-1%299

a%5Bn%5D=-12%2B9%28n-1%29

a%5Bn%5D=-12%2B9n-9

a%5Bn%5D=9n-21  <-- the general term

Edwin