Which sequence would be generated using the general term an=2*3^n-1

Question

a

5, 35, 215, 1295, ...

 b

4, 16, 52, 430, ...

 c

2, 6, 18, 54, ...

 d

1, 6, 36, 216, ...

Answer 1

Let n represent 1,2,3,4,..., infinity

If we substitute our n-values into the equation 2 * 3^n-1 it would look like this:

n = 1 --> 2*3^1-1 = 2*3⁰ = 2*1 = 2

n = 2 --> 2*3^2-1 = 2*3¹ = 2*3 = 6

n = 3 --> 2*3^3-1 = 2*3² = 2*9 = 18

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.

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and so on and so forth.

Therefore the correct answer is option c.

Answer 2

c and d are geometric with common ratios of 3 and 6

a and b are not geometric

an = 2x3^n-1 is not geometric, a=2, but 3^n-1 is not a common ratio, so the answer has to be either a or b