Question

Find the indicated sum for each sequence. S9 of –9, 36, –144, 576, ... A –585 B –471,861 C 1,887,435 D –471,852

Answer 1

Answer: Choice B)  -471,861

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Explanation:

This is a geometric sequence because each new term is found by multiplying the last term by -4.

The common ratio is r = -4. The first term is a = -9. We want to sum up n = 9 terms.

Use the geometric nth partial sum formula below to plug in the terms mentioned

$S_n = \frac{a*(1-r^n)}{1-r}\\\\S_9 = \frac{-9*(1-(-4)^9)}{1-(-4)}\\\\S_9 = \frac{-9*(1-(-262144))}{1+4}\\\\S_9 = \frac{-9*(1+262144)}{1+4}\\\\S_9 = \frac{-9*(262145)}{5}\\\\S_9 = \frac{-2359305}{5}\\\\S_9 = -471,861$