israelgonzalez1212
Answered

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What is the explicit formula for the geometric sequence with this recursive
formula?
a =
8
2.-1
(
O A... ----(3)
O B.
11
1
6
• (-4)(n-1)
OC. ,- 1.(-6)(n-1)
=
OD. 2, --5•()
160

What Is The Explicit Formula For The Geometric Sequence With This Recursive Formula A 8 21 O A 3 O B 11 1 6 4n1 OC 16n1 OD 2 5 160 class=

Sagot :

AliceBrainly21

Answer:

D)

[tex]an = -6 \times {( \frac{1}{4} )}^{n - 1} [/tex]

Step-by-step explanation:

(See the picture)

View image AliceBrainly21
abidemiokin

The explicit formula is given as [tex]T_n=-6(\frac{1}{4} )^{n-1}[/tex]

Geometric and recursive functions

The general explicit formula for a geometric sequence is expressed as:

  • [tex]T_n=ar^{n-1}[/tex]

Given the following recursive functions:

[tex]a_1=-6\\ a_n=a_{n-1}\cdot\frac{1}{4} [/tex]

Get the next two terms:

[tex]a_2=a_{1}\cdot\frac{1}{4} \\ a_2=-6\cdot\frac{1}{4} \\ a_2=\frac{-3}{2} [/tex]

For the third term:

[tex]a_3=a_{2}\cdot\frac{1}{4} \\ a_3=\frac{-3}{2} \cdot\frac{1}{4} \\ a_3=\frac{-3}{8} [/tex]

The common ratio for the sequence will be [tex]\frac{1}{4} [/tex]

The explicit formula is given as [tex]T_n=-6(\frac{1}{4} )^{n-1}[/tex]

Learn more on explicit functions here: https://brainly.com/question/10308651

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