The Fibonacci sequence is defined by a_1 = 1, | vedclass

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(A) Given $a_1 = 1, a_2 = 1$ and $a_n = a_{n-1} + a_{n-2}$ for $n > 2$.Calculating the first six terms:$a_3 = a_2 + a_1 = 1 + 1 = 2$$a_4 = a_3 + a_2 =

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$1, 2, \frac{3}{2}, \frac{5}{3}, \frac{8}{5}$

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(A) Given $a_1 = 1, a_2 = 1$ and $a_n = a_{n-1} + a_{n-2}$ for $n > 2$.Calculating the first six terms:$a_3 = a_2 + a_1 = 1 + 1 = 2$$a_4 = a_3 + a_2 = 2 + 1 = 3$$a_5 = a_4 + a_3 = 3 + 2 = 5$$a_6 = a_5 + a_4 = 5 + 3 = 8$Calculating the ratios $\frac{a_{n+1}}{a_n}$ for $n = 1, 2, 3, 4, 5$:For $n = 1: \frac{a_2}{a_1} = \frac{1}{1} = 1$For $n = 2: \frac{a_3}{a_2} = \frac{2}{1} = 2$For $n = 3: \frac{a_4}{a_3} = \frac{3}{2}$For $n = 4: \frac{a_5}{a_4} = \frac{5}{3}$For $n = 5: \frac{a_6}{a_5} = \frac{8}{5}$The sequence of ratios is $1, 2, \frac{3}{2}, \frac{5}{3}, \frac{8}{5}$.

The Fibonacci sequence is defined by $a_1 = 1, a_2 = 1$ and $a_n = a_{n-1} + a_{n-2}$ for $n > 2$. Find the sequence of ratios $\frac{a_{n+1}}{a_n}$ for $n = 1, 2, 3, 4, 5$.

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