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

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1 Answer
Jan 6, 2018

a_2014=4/5a2014=45

Explanation:

We know that:
a_1=2a1=2
a_2=5a2=5
a_(n+2)=(1+a_(n+1))/a_nan+2=1+an+1an

Using this, we can find:
a_3=(1+5)/2=6/2=3a3=1+52=62=3

a_4=(1+3)/5=4/5a4=1+35=45

a_5=(1+4/5)/3=(5/5+4/5)/3=(9/5)/3=9/15=3/5a5=1+453=55+453=953=915=35

a_6=(1+3/5)/(4/5)=(5/5+3/5)/(4/5)=(8/5)/(4/5)=8/5*5/4=8/4=2a6=1+3545=55+3545=8545=8554=84=2

a_7=(1+2)/(3/5)=3/(3/5)=3-:3/5=3*5/3=5a7=1+235=335=3÷35=353=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