SOLUTION: Select the option for "?" that continues the pattern 2,7,26,101,400,? 7,16,8,27,9,? 7,21,8,72,9,?

Algebra ->  Sequences-and-series -> SOLUTION: Select the option for "?" that continues the pattern 2,7,26,101,400,? 7,16,8,27,9,? 7,21,8,72,9,?      Log On


   

Question 971325: Select the option for "?" that continues the pattern
2,7,26,101,400,?
7,16,8,27,9,?
7,21,8,72,9,?
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
2,7,26,101,400,?
The recursion formula seems to be:

4%2Aa%5Bn%5D-n%22%22=%22%22a%5Bn%2B1%5D

4%2A2-1%22%22=%22%228-1%22%22=%22%227

4%2A7-2%22%22=%22%2228-2%22%22=%22%2226

4%2A26-3%22%22=%22%22104-3%22%22=%22%22101

4%2A101-4%22%22=%22%22404-4%22%22=%22%22400

4%2A400-5%22%22=%22%221600-5%22%22=%22%221595

Answer: 1595

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7,16,8,27,9,?
The odd-numbered terms are going 7, 8, 9, 10, ...
The even numbered terms are going 16,27, which is 8*2,9*3,so 10*4

Answer: 10*4 = 40

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7,21,8,72,9,?
The odd-numbered terms are going 7, 8, 9, 10, ... 
The even-numbered terms are going 7×3¹, 8×3², 9×3³, 10×3⁵, ..

Answer:  9×3³ = 9×27 = 243

Edwin