SOLUTION: I have to write a formula for a sequence of numbers whos tenth term is 75. Our teacher (a substitute) didn't really explain how to do this. Can you help me?

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Question 827422: I have to write a formula for a sequence of numbers whos tenth term is 75. Our teacher (a substitute) didn't really explain how to do this. Can you help me?
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
Use the formula for the nth term of an arithmetic sequence

an = a1 + (n-1)d

with n=10  

a10 = a1 + (10-1)d

a10 = a1 + 9d

Substitute 75 for a10

75 = a1 + 9d

75 - a1 = 9d 

Since the right side is 9d, pick a number for a1
so that the left side will be a multiple of 9.  You don't
have to, but that's the way to avoid fractions.  If we pick
a1 to be 3, the left side will be 72 and that
is divisible by 9.

So let's pick a1 = 3

75 - 3 = 9d
    72 = 9d
     8 = d

So substitute a1 = 3 and d = 8 in

an = a1 + (n-1)d

an = 3 + (n-1)(8)

an = 3 + 8n-8

an = 8n - 5     <-- answer

Then the sequence goes:

3,11,19,27,35,43,51,59,67,75,83,91,99,107,...

Notice that the tenth term is 75.

You could give other answers by choosing different 
numbers for a1.

Edwin