The recursive formula would be
[tex]g_n=g_{n-1}\times 2[/tex].
The explicit formula given is in the form
[tex]g_n=g_1 \times r^{n-1}[/tex]
We can manipulate this formula to find the initial value as well as the growth rate:
[tex]g_n=g_1 \times r^{n-1} = g_1 \times r^n \times r^{-1}
\\
\\=g_1 \times r^n \times \frac{1}{r}
\\
\\=g_1 \times \frac{1}{r} \times r^n= \frac{g_1}{r}\times r^n[/tex]
Viewing our equation in this form, we know that
[tex]\frac{g_1}{r} = 25
\\
\\\text{ and } r=2[/tex]
which tells us that g₁ = 50.
Since r = 2, we can write our recursive formula:
[tex]g_n=g_{n-1}\times 2[/tex]
