Question

Find the 11th term of the geometric sequence of 6,-18,54...

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

In this sequence, our common ratio is -3 (each value is -3 times the previous value). The first (or 1th) term of the sequence is 6, so we can form our equation:

$y=6(-3)^(^x^-^1^)$

Now we have to find the 11 term. To do so, we plug 11 into our equation where the x would be. Once that's done, we do the math as follows:

$y=6(-3)^(^1^1^-^1^)$ (plug in)

$y=6(-3)^(^1^0^)$ (simplify by subtracting 1 from 11 to get 10)

$y=6(59049)$ (simplify by calculating 3 to the power of 10 to get 59049)

$y=354294$ (solve by multiplying 6 by 59040 to get 354294

Therefore, our 11th term in the sequence is 354394.