Respuesta :
Answer:
[tex]a_5 = 21[/tex]
Step-by-step explanation:
Arithmetic sequence:
In an arithmetic sequence, the difference between consecutive terms is always the same, and this difference is called common difference.
The nth term of an arithmetic sequence is given by:
[tex]a_n = a_1 + d(n-1)[/tex]
In which [tex]a_1[/tex] is the first term and d is the common difference.
In this question:
[tex]a_1 = 5, d = 4[/tex]. So
[tex]a_n = a_1 + d(n-1)[/tex]
[tex]a_n = 5 + 4(n-1)[/tex]
Find the value of a_5
[tex]a_n = 5 + 4(n-1)[/tex]
[tex]a_5 = 5 + 4(5-1) = 5 + 16 = 21[/tex]
So
[tex]a_5 = 21[/tex]
The [tex]a_{5}[/tex] term of an arithmetic sequence is 21.
What is an arithmetic sequence?
An arithmetic sequence is a sequence of numbers where the difference between consecutive terms is constant, and this difference is called the common difference.
The nth term of the sequence is given by
[tex]\rm a_{n} =a_{1} + (n-1)d\\[/tex]
[tex]a_{1}[/tex]= the first term of the sequence and d is a common difference.
[tex]\rm a_{1} = 5, d=4\\\rm a_{n} =a_{1} + (n-1)d\\\rm a_{n} = 5 + 4(n-1)\\\rm a_{5} = 5 + 4(5-1)\\\rm a_{5} = 21[/tex]
Therefore, The [tex]a_{5}[/tex] term of an arithmetic sequence is 21.
Learn more about arithmetic here;
https://brainly.com/question/2171130
