Step-by-step explanation:
[tex] = \sum \limits_{n = 1}^{7} ( - 2. {6}^{n - 1} )[/tex]
[tex] = \sum \limits_ {n = 1}^{n_{ \text{max}}} (a_1. {r}^{n - 1} )[/tex]
[tex] \: [/tex]
[tex]a_1 = - 2[/tex]
[tex]n = 7[/tex]
[tex]r = 6 \to r >1[/tex]
[tex] \: [/tex]
• Find S7.
[tex]s_n = a_1.( \frac{ {r}^{n} - 1}{r - n} )[/tex]
[tex]s_7 = - 2.( \frac{ {6}^{7} - 1 }{6 - 1} )[/tex]
[tex]s_7 = - 2.( \frac{279.936 - 1}{5} )[/tex]
[tex]s_7 = - 2.( \frac{279.935}{5} )[/tex]
[tex]s_7 = - 2 \: . \: 55.987[/tex]
[tex]s_7 = - 111.974[/tex]
The answer is B.
