A sequence is an arrangement of any objects or a set of numbers in a particular order followed by some rule. If [tex]a_{1},a_{2},a_{3},a_{4}, ...,a_{n}[/tex] denote the terms of a sequence, then[tex]1,2,3,4,..., n[/tex] denotes the position of the term.
A sequence can be defined based on the number of terms i.e. either finite sequence or infinite sequence.
It [tex]a_{1},a_{2},a_{3},a_{4}, ..., etc.[/tex]is a sequence, then the corresponding series is the sum of all of the terms on the sequence.
Some of the most common examples of sequences are:
∴Arithmetic Sequences = A sequence in which every term is created by adding or subtracting a definite number to the preceding number is an arithmetic sequence that is Common Difference (d)
∴Geometric Sequences = The order in which each term is obtained by multiplying or dividing a certain number by a previous number is known as a geometric sequence, such multiplied or divided numbers are called ratio (r).
From the Question, It can be concluded that what is meant is arithmetics sequence.
Answers & Comments
A sequence is an arrangement of any objects or a set of numbers in a particular order followed by some rule. If [tex]a_{1},a_{2},a_{3},a_{4}, ...,a_{n}[/tex] denote the terms of a sequence, then[tex]1,2,3,4,..., n[/tex] denotes the position of the term.
A sequence can be defined based on the number of terms i.e. either finite sequence or infinite sequence.
It [tex]a_{1},a_{2},a_{3},a_{4}, ..., etc.[/tex]is a sequence, then the corresponding series is the sum of all of the terms on the sequence.
Series is denoted by [tex]S_{n}[/tex]
[tex]S_{n}= a_{1}+a_{2}+a_{3}+a_{4}+...+a_{n}[/tex].
Some of the most common examples of sequences are:
∴Arithmetic Sequences = A sequence in which every term is created by adding or subtracting a definite number to the preceding number is an arithmetic sequence that is Common Difference (d)
∴Geometric Sequences = The order in which each term is obtained by multiplying or dividing a certain number by a previous number is known as a geometric sequence, such multiplied or divided numbers are called ratio (r).
From the Question, It can be concluded that what is meant is arithmetics sequence.
Arithmetic Sequences
[tex]a_{n}= a + (n-1)*d[/tex]
if, [tex]a=5, d=4[/tex]
then, [tex]a_{23}=a+(23-1)*d\\a_{23}=5+(22*4)\\a_{23}=5+88\\a_{23]= 93\\\\[/tex]
To learn more about the sequence is here :
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