Question

PLEASE HELP ASAP

Answer 1

we conclude that the sequence has 8 terms.

How to get the number of terms in the sequence?

Here we have the geometric sequence:

2/81, 4/27, 8/9, ..., 6912

Notice that each term is equal to 6 times the previous term, such that:

2/81*6 = 4/27

4/27*6 = 8/9

Then the n-th term is equal to:

$a_n = a_1*r^{n-1}$

Where in this case:

$a_1 = 2/81\\\\r = 6$

Now we need to find the value of n such that:

$(2/81)*6^{n-1} = 6912\\\\6^n = 6*6812*(81/2) = 1,679,616$

If we apply the natural logarithm to both sides, then:

$n*ln(6) = ln(1,679,616)\\n = ln(1,679,616)/ln(6) = 8$

Then we conclude that the sequence has 8 terms.

If you want to learn more about geometric sequences:

brainly.com/question/1509142

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