SOLUTION: Hello, I need help finding the explicit formula for this problem. I'm fairly certain that I got the recursive one right, but I cannot figure out how to write the explicit formula.

Algebra ->  Test -> SOLUTION: Hello, I need help finding the explicit formula for this problem. I'm fairly certain that I got the recursive one right, but I cannot figure out how to write the explicit formula.       Log On


   

Question 1085106: Hello, I need help finding the explicit formula for this problem. I'm fairly certain that I got the recursive one right, but I cannot figure out how to write the explicit formula. Any help would be much appreciated.
Thanks in advance for your help!

1. Find both a recursive rule and an explicit rule that will generate the values in the table below, provided that a0 = 3/2.
n: 1---- 2---- 3---- 4---- 5---- 6
an: 2---- 3---- 5---- 9----17----33

Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
+a%5B1%5D+=+2a%5B0%5D+-+1+
+a%5B2%5D+=+2a%5B1%5D+-+1+
…
+a%5Bn%5D+=+2a%5Bn-1%5D+-+1+
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To find the explicit formula, let's just do some substitutions on the first few values to see if it can be generalized:
+a%5B1%5D+=+2a%5B0%5D+-+1+
+a%5B2%5D+=+2a%5B1%5D+-+1+=+2%282a%5B0%5D+-+1%29+-+1+=+%282%5E2%29%2Aa%5B0%5D+-+2+-+1+

Those last three terms look a lot like +2%5En+-+1+ (n=3 and the numbers add to 7)
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I claim that +a%5Bn%5D+=+%282%5En%29a%5B0%5D+-+%282%5En-1%29+
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Check: +a%5B4%5D+=+%282%5E4%29%283%2F2%29+-+%282%5E4-1%29+=+24+-+15+=+9+ (ok)