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Answer: Choice B) 19684</h3>
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Explanation:
We have a geometric sequence with a = 4 as the first term and r = -3 as the common ratio.
Use the formula below to find the nth partial sum
Sn = a*(1-r^n)/(1-r)
S9 = 4(1-(-3)^9)/(1-(-3))
S9 = 4(1-(-19683))/(1+3)
S9 = 4(1+19683)/(1+3)
S9 = 4(19684)/(4)
S9 = 78736/4
S9 = 19684
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A longer method would be to generate the 9 terms of this sequence. We do so by multiplying every term by -3 to get the next term
The first nine terms are {4, -12, 36, -108, 324, -972, 2916, -8748, 26244}
and they add to
4 + (-12) + 36 + (-108) + 324 + (-972) + 2916 + (-8748) + 26244 = 19684
which confirms our answer. I recommend using the formula however because n = 9 terms is quite a bit to add up.
