Answer:
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3a - 4b = 21
check (-2 , -3)
3(-2) -4(-3) =21
-6 +12 = 21
6 does not = 21 so NO
check (0 , 7)
3(0) -4(7) =21
0-28=21
-28 does not equal 21 so NO
check (-3 , -2)
3(-3) -4(-2) =21
-9 +8 = 21
1 does not = 21 so NO
check (7 , 0)
3(7) -4(0) =21
21 = 21
Choice D
All three series converge, so the answer is D.
The common ratios for each sequence are (I) -1/9, (II) -1/10, and (III) -1/3.
Consider a geometric sequence with the first term <em>a</em> and common ratio |<em>r</em>| < 1. Then the <em>n</em>-th partial sum (the sum of the first <em>n</em> terms) of the sequence is

Multiply both sides by <em>r</em> :

Subtract the latter sum from the first, which eliminates all but the first and last terms:

Solve for
:

Then as gets arbitrarily large, the term
will converge to 0, leaving us with

So the given series converge to
(I) -243/(1 + 1/9) = -2187/10
(II) -1.1/(1 + 1/10) = -1
(III) 27/(1 + 1/3) = 18
Ahhh I think that is cheating?
Soz I know the anaswer but I cant tell you have to do by your self to learn you can't always ask for answers :<