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]T_n = a + (n-1)d[/tex]
[tex]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]T_n = a ~ r^{n-1}[/tex]
[tex]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!
Since the question is not clearly stated, then let me assume the problem is to convert 1.83838383... as a fraction.
Let :
X = 1.8383838383... = 1.83
100X = 183.83838383... = 183.83
100X - X = 183.83 - 1.83
99X = 182
X = 182 ÷ 99
[tex]\large {\boxed {X = \frac{182}{99} } }[/tex]
If the problem is to convert 1.833333... as a fraction , then :
Let :
X = 1.833333... = 1.83
10X = 18.33333... = 18.3
100X = 183.3333... = 183.3
100X - 10X = 183.3 - 18.3
90X = 165
X = 165 ÷ 90
[tex]\large {\boxed {X = \frac{11}{6} } }[/tex]
If the problem is to convert 1.83183183183... as a fraction , then :
Let :
X = 1.83183183183... = 1.83183
100X = 183.183183... = 183.183
100000X = 183183.183... = 183183.183
100000X - 100X = 183183.183 - 183.183
99900X = 183000
X = 183000 ÷ 99900
[tex]\large {\boxed {X = \frac{610}{333} } }[/tex]
Grade: Middle School
Subject: Mathematics
Chapter: Arithmetic and Geometric Series
Keywords: Arithmetic , Geometric , Series , Sequence , Difference , Term
