Fibonacci Sequence

Number Theory Level 3

$T_{n}$ represents the $n^{th}$ term of the Fibonacci Sequence $1,1,2,3,5,8,13,21,... (T_{n}=T_{n-1}+T_{n-2})$

If $a=\lim_{n \rightarrow \infty} \frac{T_{n+1}}{T_{n}}$ ,

Find the value of $(2a-1)^{2}.$