Answer:
The correct answer option is B. [tex] a _ 1 = -4[/tex], [tex] r = \frac{1}{2} [/tex], [tex] n = 6 [/tex], [tex] S_n = -\frac{63}{8} [/tex].
Step-by-step explanation:
We are given the following:
[tex]6_\sum_{n=1}[/tex] [tex]-4(\frac{1}{2} )^{n-1}[/tex]
and we are to identify the first term ( [tex] a _ 1 [/tex] ), common ratio ( [tex] r [/tex] ), number of terms ( [tex] n [/tex] ) and the sum of n terms ( [tex] S_n [/tex] ).
Here, [tex] a _ 1 = -4[/tex],
[tex] r = \frac{1}{2} [/tex],
[tex] n = 6 [/tex]; and
[tex]S_n = \frac{a_1(1-r^n)}{(1-r)} = \frac{-4(1-0.5^6)}{(1-0.5)} = -\frac{63}{8}[/tex]
