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

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

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.

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.

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:

The iterative rule for the sequence:

Grade: Middle School

Subject: Mathematics

Chapter: Arithmetic and Geometric Series

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

9

step-by-step explanation: