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.
[tex]\boxed{T_n = a + (n-1)d}[/tex]
[tex]\boxed{S_n = \frac{1}{2}n ( 2a + (n-1)d )}[/tex]
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.
[tex]\boxed{T_n = a ~ r^{n-1}}[/tex]
[tex]\boxed{S_n = \frac{a( 1 - r^n ) }{1 - r}}[/tex]
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:
[tex]r = a_2 \div a_1 = 4 \div 8 = 0.5[/tex]
[tex]\texttt{ }[/tex]
The iterative rule for the sequence:
[tex]a_n = a_1 \cdot~ r^{n-1}[/tex]
[tex]a_n = 8 \cdot~ (0.5)^{n-1}[/tex]
[tex]\texttt{ }[/tex]
Learn more
- Geometric Series : https://brainly.com/question/4520950
- Arithmetic Progression : https://brainly.com/question/2966265
- Geometric Sequence : https://brainly.com/question/2166405
Answer details
Grade: Middle School
Subject: Mathematics
Chapter: Arithmetic and Geometric Series
Keywords: Arithmetic , Geometric , Series , Sequence , Difference , Term
