Mathematics, 24.07.2019 16:40 lexie223

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

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Answer from: hallkayleel0lozgxtq

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

Answer from: katiek451

The explicit rule for this geometric sequence is $\boxed{2 \times {{\left( 3 \right)}^{n - 1}}}$ . 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,

$\boxed{r =\dfrac{{{a_2}}}{{{a_1}}}}$

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

$\boxed{{a_n} = a \times {r^{n - 1}}}$ …… (1)

Given:

The sequence is 2, 6, 18, 54 ,…

The options are as follows,

(a). ${a_n} = 3 \cdot 2n - 1$

(b). ${a_n} = 2 \cdot 3n$

(c). ${a_n} = 2 \cdot 3n - 1$

(d). ${a_n} = 3 \cdot 2n$

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.

$\begin{aligned}r&=\frac{{{a_2}}}{{{a_1}}}\\&=\frac{6}{2}\\&= 3\\\end{aligned}$

The common ratio is 3.

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

${a_n} = 2 \times {\left( 3 \right)^{n - 1}}$

The explicit rule for this geometric sequence is $\boxed{2 \times {{\left( 3 \right)}^{n - 1}}}.$ 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.

Answer from: Quest

answer: i think it is (1,-2)

Answer from: Quest

I’m not sure about that

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