Question

the graph shows the first five terms in a geometric sequence what is the iterative rule for the sequence​

Answer 1

The iterative rule for the sequence is a_n = 8 · ( 0.5 )ⁿ ⁻ ¹

Further explanation

Firstly , let us learn about types of sequence in mathematics.

Arithmetic Progression is a sequence of numbers in which each of adjacent numbers have a constant difference.

$\boxed{T_n = a + (n-1)d}$

$\boxed{S_n = \frac{1}{2}n ( 2a + (n-1)d )}$

Tn = n-th term of the sequence

Sn = sum of the first n numbers of the sequence

a = the initial term of the sequence

d = common difference between adjacent numbers

Geometric Progression is a sequence of numbers in which each of adjacent numbers have a constant ration.

$\boxed{T_n = a ~ r^{n-1}}$

$\boxed{S_n = \frac{a( 1 - r^n ) }{1 - r}}$

Tn = n-th term of the sequence

Sn = sum of the first n numbers of the sequence

a = the initial term of the sequence

r = common ratio between adjacent numbers

Let us now tackle the problem!

Given:

a₁ = 8

a₂ = 4

a₃ = 2

a₄ = 1

Solution:

Firstly , we find the ratio by following formula:

$r = a_2 \div a_1 = 4 \div 8 = 0.5$

$\texttt{ }$

The iterative rule for the sequence:

$a_n = a_1 \cdot~ r^{n-1}$

$a_n = 8 \cdot~ (0.5)^{n-1}$

$\texttt{ }$

Learn more

• Geometric Series : brainly.com/question/4520950
• Arithmetic Progression : brainly.com/question/2966265
• Geometric Sequence : brainly.com/question/2166405

Answer details

Grade: Middle School

Subject: Mathematics

Chapter: Arithmetic and Geometric Series

Keywords: Arithmetic , Geometric , Series , Sequence , Difference , Term