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?

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Answer 1 · 2017-06-13T02:57:00

Given: #a_1 = 81# and #a_(k+1) = 1/3a_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#