Question

2) 4 - 12 + 36 – 108..., n = 9 A) 1 B) 19684 C) 23218 D) 21549

Answer 1

Answer: Choice B) 19684

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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.

Answer 2

I think the answer is A