Answer:
12
Step-by-step explanation:
The given geometric series is
[tex] \sum_{n = 1}^{ \infty} 12( { - \frac{1}{9} })^{n - 1} [/tex]
We want to determine the first term of this geometric series.
Recall that the explicit formula is
[tex] a_{n} = 12( { - \frac{1}{9} })^{n - 1} [/tex]
To find the first term, we put n=1 to get:
[tex]a_{1} = 12( { - \frac{1}{9} })^{1 - 1} [/tex]
This gives us:
[tex]a_{1} = 12( { - \frac{1}{9} })^{0}[/tex]
[tex]a_{1} = 12(1) = 12[/tex]
Therefore the first term is 12
