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

 Apr 25, 2022
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Sequence  is   defined as    an  =  2an-1

 

1 , 2  , 4  ,  8 .......   etc

 

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

 

So

 

a23  =  2^(23 -1)  = 2^22   ⇒   p   =  22

 

cool cool cool

 Apr 25, 2022

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