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A sequence with a_1 = 1 is defined by the recurrence relation a_{n+1} = 2^n + a_n for all natural numbers n. If a_{23} = p, then what is p?

 Apr 6, 2022
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Note that the first few terms of the sequence are :

 

1, 3 , 7 , 15 , 31 , 63 , 127  ..... 

 

The  terms are   2^n    - 1     where  n  =  the nth term 

 

a23 =  p =   2^23 - 1  =   8388607

 

cool cool cool

 Apr 6, 2022

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