SOLUTION: complete the series 3/2,9/4,3,

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Question 915764: complete the series 3/2,9/4,3,
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!

a%5B2%5D-a%5B1%5D=9%2F4-3%2F2=9%2F4-6%2F4=3%2F4
a%5B3%5D-a%5B2%5D=3-9%2F4=12%2F4-6%2F4=3%2F4

So it's an arithmetic sequence with d=3%2F4 and a%5B1%5D=3%2F2 

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

a%5Bn%5D=3%2F2%2B%28n-1%29%2Aexpr%283%2F4%29

Clear of fractions by multiplying through by 4

4a%5Bn%5D=6%2B%28n-1%293

4a%5Bn%5D=6%2B3%28n-1%29

4a%5Bn%5D=6%2B3n-3=3%2B3n=3%281%2Bn%29

Solve for an

a%5Bn%5D=3%281%2Bn%29%2F4

Edwin