What is the explicit rule for this geometric sequence? 2, 6, 18, 54, … an=3⋅2n−1 an=2⋅3n an=2⋅3n−1 an=3⋅2n

To find the explicit formula of geometric sequences, you'll need to find a formula for the nth term.

In symbols, the nth term of a geometric sequence is:  tn  =  a·rn-1.

a = first term     and     r = common ratio

To find the common ratio, divide any term by its preceding term.

Example:  2, 6, 18, 54, 162, ...

a = first term = 2

r = common ratio = 6/3 = 2 (this will be the same anywhere you begin:  162/54 = 3, 54/18 = 3, 18/6 = 3, etc.)

So, the explicit formula is:  tn  =  2·3n-1

Each explicit formula will have the exponent "n-1".

Your answer would be; tn  =  2·3n-1

The explicit rule for this geometric sequence is . Option (c) is correct.

Further Explanation:

If the first term a and the second term ar is known then, the value of r can be obtained as follows,

The nth term of the geometric sequence can be obtained as,

           …… (1)

Given:

The sequence is ,…

The options are as follows,

(a).

(b).

(c).

(d).

Explanation:

The first term of the sequence is 2, second term of the sequence, is 6, third term is 18.

The common ratio r can be obtained as follows.

The common ratio is 3.

Substitute 3 for r and 2 for a in equation (1) to obtain the nth term.

The explicit rule for this geometric sequence is Option (c) is correct.

Learn more:

1. Learn more about inverse of the functionhttps://.

2. Learn more about equation of circle .

3. Learn more about range and domain of the function

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Geometric progression

Keywords: geometric sequence, explicit rule, common ratio, first term, second term, sum of geometric sequence, nth term of the geometric sequence.

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