How do you write the first five terms of the sequence defined recursively a_1=81,a_(k+1)=1/3a_k, then how do you write the nth term of the sequence as a function of n?

raapjeqp

raapjeqp

Answered question

2022-10-25

How do you write the first five terms of the sequence defined recursively a 1 = 81 , a k + 1 = 1 3 a k , then how do you write the nth term of the sequence as a function of n?

Answer & Explanation

Dobricap

Dobricap

Beginner2022-10-26Added 14 answers

Given a 1 = 81 , a k + 1 = 1 3 a k ,
Starting with the first term:
a 1 = 81 = ( 1 3 ) 0 81
a 2 = ( 1 3 ) 81 = ( 1 3 ) 1 81
a 3 = ( 1 3 ) a 2 = ( 1 3 ) ( 1 3 ) 81 = ( 1 3 ) 2 81
a 4 = ( 1 3 ) a 3 = 1 3 ( 1 3 ) 2 81 = ( 1 3 ) 3 81
The equation for the nth term is:
a n = ( 1 3 ) n - 1 81

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