Question

"What is the 12th term in the geometric sequence -9,27,-81...?​​

Answer 1

Step-by-step explanation:

You have already identified/ you know it is a Geometric series.

Which means, this series has a common ratio, which can be figured out by dividing an nth term and an n-1 th term.

Implies, common ratio = 27/(-9) = (-81)/27 = -3

Now, the nth term of any GP is given by...

$an \: = \: a1 \times {r}^{n - 1}$

where A1 is your initial/ first term of series.

Thus, your 12th term is..

$A12 = (-9) \: \times \: { - 3}^{11}$

Now (-3)^11 is (apparently) equal to 177,147... so multiply that by -9 and that is your answer.

Please note I've no idea why they gave such a huge exponent, but I used the calculator for (-3)^11.

Best regards.

Answer 2

Answer:

You have already identified/ you know it is a Geometric series.

Which means, this series has a common ratio, which can be figured out by dividing an nth term and an n-1 th term.

Implies, common ratio = 27/(-9) = (-81)/27 = -3

Now, the nth term of any GP is given by...

an \: = \: a1 \times {r}^{n - 1}an=a1×rn−1

where A1 is your initial/ first term of series.

Thus, your 12th term is..

A12 = (-9) \: \times \: { - 3}^{11}A12=(−9)×−311

Now (-3)^11 is (apparently) equal to 177,147... so multiply that by -9 and that is your answer.

Please note I've no idea why they gave such a huge exponent, but I used the calculator for (-3)^11.

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