The first 4 terms in the sequence are :
A) { 4 , 0.8 , 0.16 , 0.032 , . . . }
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:
a = 4
r = 0.2
Solution:
[tex]T_n = a ~ r^{n-1}[/tex]
[tex]T_1 = 4 \times 0.2^{1-1} = 4 \times 1 = 4[/tex]
[tex]T_2 = 4 \times 0.2^{2-1} = 4 \times 0.2 = 0.8[/tex]
[tex]T_3 = 4 \times 0.2^{3-1} = 4 \times 0.04 = 0.16[/tex]
[tex]T_4 = 4 \times 0.2^{4-1} = 4 \times 0.008 = 0.032[/tex]
Therefore , the first 4 terms in the sequence are :
A) { 4 , 0.8 , 0.16 , 0.032 , . . . }
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
