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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} = 2^p, then what is p?

 Jul 11, 2022
 #1
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a1 = 2^0

a2 = 2^1 * 1   = 2^1

a3 = 2^2 * 2^1  = 2^3

a4  = 2^3 * 2^3  = 2^6

a5 = 2^4 * 2^6  = 2^10

a6 = 2^5 * 2^10 = 2^15

.......

 

The nth term is  given by   2 ^ ( n * (n-1)  / 2)

 

a23  =  2 ^ (23 * 22  / 2)  =   2^(23 * 11)  =  2^253   ⇒   p =  253

 

 

cool cool cool

 Jul 11, 2022

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