Calculating n t h n^{th} term

Number Theory Level pending

Find the 2 1 t h 21^{th} term of the sequence 1 , 3 , 8 , 20 , 48 , 112 , 368 , . . . . . 1,3,8,20,48,112,368,.....


The answer is 11534336.

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1 solution

Maggie Miller
Aug 2, 2015

The k k -th term in this sequence is 2 k 2 ( k + 1 ) 2^{k-2}\cdot(k+1) .

Therefore, the 2 1 st 21^{\text{st}} term is 2 19 22 = 11534336 2^{19}\cdot22=\boxed{11534336} .

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