Solve -1=4a_{1}q-1=frac{a_{1}(19^n)}{1-9}

$$- 1 = 4 a _ { 1 } q - 1 = \frac { a _ { 1 } ( 19 ^ { n } ) } { 1 - 9 }$$

Evaluate (complex solution)

$$-1=4a_{1}q-1\text{ and }4a_{1}q-1=-\frac{a_{1}\times 19^{n}}{8}$$

Solve for q

$$q=0$$

$$a_{1}=\frac{8}{19^{n}}$$

Solve for n

$$n=-\frac{\ln(a_{1})-3\ln(2)}{\ln(19)}$$

$$a_{1}>0\text{ and }q=0$$