ANSWER
[tex]a_1=12[/tex]
EXPLANATION
We were given the geometric series,
[tex] {\sum_{n=1}}^{ \infty } 12 \:( { - \frac{1}{9} })^{n - 1} [/tex]
This implies that, the nth term is
[tex]a_n=12( - \frac{1}{9} ) ^{n - 1} [/tex]
To find the first term, we put
[tex]n = 1[/tex]
in to the nth term.
This implies that,
[tex]a_1=12( - \frac{1}{9} ) ^{1- 1} [/tex]
We simplify to obtain,
[tex]a_1=12( - \frac{1}{9} ) ^{0} [/tex]
We know that, any non zero number raised to the power zero is 1.
[tex]a_1=12(1)[/tex]
This simplifies to,
[tex]a_1=12[/tex]
The correct answer is option D
