What is the value of (see below)?

Question

Consider the sequence that starts with #a_1 = 7# and #a_2 = 8#, with #a_n = (1 + a_(n−1))/a_(n−2) #for #n ≥ 3#. What is the value of #a_2017#?

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Answer 1 · 2018-03-05T08:49:03

#a_2017=8#

We know the following:
#a_1=7#
#a_2=8#
#a_n=(1+a_(n-1))/a_(n-2)#

So:
#a_3=(1+8)/7=9/7#
#a_4=(1+9/7)/8=2/7#
#a_5=(1+2/7)/(9/7)=1#
#a_6=(1+1)/(2/7)=7#
#a_7=(1+7)/1=8#

#a_n=[(5n+1,5n+2,5n+3,5n+4,5n),(7,8,9/7,2/7,1)],ninZZ#

Since, #2017=5n+2#, #a_2017=8#