Answer: C) -81/2
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Work Shown:
a = -27 = first term
r = 1/3 = common ratio, note how this is between -1 and 1
We start with -27 and multiply by 1/3 each time to get the next term
S = infinite sum
S = a/(1-r), which only works because -1 < r < 1 is true
S = -27/(1-1/3)
S = -27/(2/3)
S = (-27/1) divided by (2/3)
S = (-27/1) times (3/2)
S = (-27*3)/(1*2)
S = -81/2
As you generate and add up the terms of the sequence, the infinite sum slowly starts to approach -81/2 = -40.5; we'll never actually achieve this sum exactly. Think of it as approaching an asymptote.
