Answer
$a_{1}$ = 1
$a_{2}$ = 1
Work Step by Step
For the $n^{th}$ term of a Fibonacci Sequence, it is represented by
$a_{n}$ = $\frac{1}{\sqrt{5}}[(\frac{1+\sqrt{5}}{2})^n$ - $(\frac{1-\sqrt{5}}{2})^n]$
So, for the first term, $a_{1}$
= $\frac{1}{\sqrt{5}}[(\frac{1+\sqrt{5}}{2})^1$ - $(\frac{1-\sqrt{5}}{2})^1]$
= $\frac{1}{\sqrt{5}}[\frac{1+\sqrt{5}}{2}$ - $(\frac{1-\sqrt{5}}{2})]$
= $\frac{1}{\sqrt{5}}[\frac{1+\sqrt{5}-1+\sqrt{5}}{2}]$
= $\frac{1}{\sqrt{5}}(\frac{2\sqrt{5}}{2})$
= $\frac{1}{\sqrt{5}} \cdot \sqrt{5}$
= 1
And, for the second term, $a_{2}$
= $\frac{1}{\sqrt{5}}[(\frac{1+\sqrt{5}}{2})^2$ - $(\frac{1-\sqrt{5}}{2})^2]$
= $\frac{1}{\sqrt{5}}[(\frac{1+\sqrt{5}}{2})$ + $(\frac{1-\sqrt{5}}{2})]$$[(\frac{1+\sqrt{5}}{2})$ - $(\frac{1-\sqrt{5}}{2})]$
= $\frac{1}{\sqrt{5}}(\frac{1+\sqrt{5}+1-\sqrt{5}}{2})
(\frac{1+\sqrt{5}-1+\sqrt{5}}{2})$
= $\frac{1}{\sqrt{5}}(\frac{2}{2})(\frac{2\sqrt{5}}{2})$
= $\frac{1}{\sqrt{5}} \cdot 1 \cdot \sqrt{5}$
= 1
Hence, the first two terms of a Fibonacci Sequence are each equal to 1.
