# SOLUTION: What is a recursive and an explicit formula for the sequence: 2/3, 4/9, 16/81 ...

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 Question 614717: What is a recursive and an explicit formula for the sequence: 2/3, 4/9, 16/81 ...Answer by Edwin McCravy(8909)   (Show Source): You can put this solution on YOUR website!```Wr'll find the explicit formula first: Sequence 1 = , , , ... That's the sequence a1=, a2=, a3=, ... The exponents follow the sequence Sequence 2: 1, 2, 4, ... That's the sequence: 20, 21, 22, ... Those exponents follow the sequence: Sequence 3: 0, 1, 2 which follow the sequence 1-1, 2-1, 3-1 which has nth term: n-1 Therefore sequence 2 has nth term: 2n-1 Therefore sequence 1 has sequence: an = That's the explicit formula. --------------------------------- So the sequence is , , , ... ---------------------------------- To find a recursion formula: Divide the (n+1)st term by the nth term: ÷ ÷ an+1 = an·()2n-1 And the complete recursion formula is: a1 = , an+1 = an+1 = an·()2n-1 Edwin```