Answer:
see below
Step-by-step explanation:
The terms being summed are of the form ...
a1(r)^(i-1)
which is the form of the general term of a geometric sequence. The summation symbol tells you the values of i range from 1 to 6, so this is the sum of 6 terms of the series. (n=6)
Comparing the form of the general term to the one shown, you can see that the leading coefficient (a1) is -4, and the common ratio (r) is 1/2. With these values in mind, the first and third answer choices are possibilities. However, the sum must be negative, since all of its terms are negative. Thus the only viable answer choice is the third one.
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<em>Check</em>
The sum of n terms of a geometric series is ...
Sn = a1(1 -r^n)/(1 -r)
For the given values, this is ...
S6 = -4(1 -(1/2)^6)/(1 -1/2) = -4(63/64)/(1/2) = -63/8
