What is the value of it? Thank you in advance.

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Answer 1 · 2018-01-06T19:22:16

#a_2014=4/5#

We know that:
#a_1=2#
#a_2=5#
#a_(n+2)=(1+a_(n+1))/a_n#

Using this, we can find:
#a_3=(1+5)/2=6/2=3#

#a_4=(1+3)/5=4/5#

#a_5=(1+4/5)/3=(5/5+4/5)/3=(9/5)/3=9/15=3/5#

#a_6=(1+3/5)/(4/5)=(5/5+3/5)/(4/5)=(8/5)/(4/5)=8/5*5/4=8/4=2#

#a_7=(1+2)/(3/5)=3/(3/5)=3-:3/5=3*5/3=5#

The sequence has a loop of 5 numbers, #((2, 5,3,4/5,3/5),(a_1,a_2,a_3,a_4,a_5))#

Since 2015 is a multiple of 5, #a_2015=3/5#

So, #a_2014=4/5#