What is the value of (see below)?

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What is the value of (see below)?

Consider the sequence that starts with $a_{1} = 7$ $a_1 = 7$ and $a_{2} = 8$ $a_2 = 8$ , with $a_{n} = \frac{1 + a_{n - 1}}{a_{n - 2}}$ $a_n = (1 + a_(n−1))/a_(n−2)$ for $n \geq 3$ $n ≥ 3$ . What is the value of $a_{2017}$ $a_2017$ ?

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Answer 1 · 2018-03-05T08:49:03

$a_{2017} = 8$ $a_2017=8$

Explanation:

We know the following:
$a_{1} = 7$ $a_1=7$
$a_{2} = 8$ $a_2=8$
$a_{n} = \frac{1 + a_{n - 1}}{a_{n - 2}}$ $a_n=(1+a_(n-1))/a_(n-2)$

So:
$a_{3} = \frac{1 + 8}{7} = \frac{9}{7}$ $a_3=(1+8)/7=9/7$
$a_{4} = \frac{1 + \frac{9}{7}}{8} = \frac{2}{7}$ $a_4=(1+9/7)/8=2/7$
$a_{5} = \frac{1 + \frac{2}{7}}{\frac{9}{7}} = 1$ $a_5=(1+2/7)/(9/7)=1$
$a_{6} = \frac{1 + 1}{\frac{2}{7}} = 7$ $a_6=(1+1)/(2/7)=7$
$a_{7} = \frac{1 + 7}{1} = 8$ $a_7=(1+7)/1=8$

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

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

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What is the value of (see below)?

Consider the sequence that starts with $a_{1} = 7$ $a_1 = 7$ and $a_{2} = 8$ $a_2 = 8$ , with $a_{n} = \frac{1 + a_{n - 1}}{a_{n - 2}}$ $a_n = (1 + a_(n−1))/a_(n−2)$ for $n \geq 3$ $n ≥ 3$ . What is the value of $a_{2017}$ $a_2017$ ?

1 Answer

Explanation:

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What is the value of (see below)?

Consider the sequence that starts with a_1 = 7a1=7a_1 = 7 and a_2 = 8a2=8a_2 = 8, with a_n = (1 + a_(n−1))/a_(n−2) an=1+an−1an−2a_n = (1 + a_(n−1))/a_(n−2) for n ≥ 3n≥3n ≥ 3. What is the value of a_2017a2017a_2017?

1 Answer

Explanation:

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Impact of this question

Consider the sequence that starts with $a_{1} = 7$ $a_1 = 7$ and $a_{2} = 8$ $a_2 = 8$ , with $a_{n} = \frac{1 + a_{n - 1}}{a_{n - 2}}$ $a_n = (1 + a_(n−1))/a_(n−2)$ for $n \geq 3$ $n ≥ 3$ . What is the value of $a_{2017}$ $a_2017$ ?