Question

What is the recursive formula when given the explicit formula for the following geometric sequence?


a_n=6(-8)^n-1

A. a_1=-8, a_n=-6a_n-1
B. a_1=6, a_n=-8a_n-1
C. a_1=-8, a_n=6a_n-1
D. a_1=6, a_n=8a_n-1

Answer 1

Answer:

B.

Step-by-step explanation:

When n = 1, we have:

$a_1 = 6\left(-8\right)^{0} = 6\times 1 = 6.$

Now, let's compare $a_{n-1}$ and $a_n$.

We see that: $a_{n-1} = 6\left(-8\right)^{n-2} = 6\left(-8\right)^{n-1}\times \left(-8\right)^{-1}.$

So, finally, substituting $a_n$ and rearranging, we get:

$a_{n-1} = \frac{a_n}{-8} \Rightarrow -8a_{n-1} = a_n.$

In actual fact, this should be expected because the ratio between two terms in the geometric sequence is the number with the exponent!

Answer 2

Option B is the correct answer. The value of a₁ = 6 and -8.aₙ₋₁ = aₙ.

What is Geometric Sequence?

A geometric sequence is a special type of sequence where the ratio of every two successive terms is a constant. This ratio is known as a common ratio of the geometric sequence.

Here, nth term of geometric sequence

        aₙ = a.rⁿ⁻¹

a₁ = 6 and r = -8

When n = 1, we have:

       a₁ = 6.(-8)¹⁻¹ = 6 X (-8)⁰ = 6

Now, let's compare aₙ₋₁ and aₙ.

We see that:  aₙ₋₁ = a.rⁿ⁻²

                            = 6. (-8)ⁿ⁻²

                           = 6 .(-8)ⁿ⁻¹ . (-8)⁻¹

                      aₙ₋₁ = aₙ/(-8)

                      -8.aₙ₋₁ = aₙ

Thus, the value of a₁ = 6 and -8.aₙ₋₁ = aₙ.

Learn more about Geometric Sequence from:

https://brainly.com/question/11266123

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