Respuesta :
Answer:
Option B is correct
[tex]a_n = 5n-1[/tex]; 499
Step-by-step explanation:
The nth term for the arithmetic sequence is given by:
[tex]a_n = a_1+(n-1)d[/tex] ....[1]
where,
[tex]a_1[/tex] is the first term
d is the common difference of two successive terms
n is the number of terms.
As per the statement:
4, 9, 14, 19, 24, 29.....
This is a arithmetic sequence.
Here, [tex]a_1=4[/tex] and d =5
Since,
9-4 = 5,
14-9 =5,
19-14 = 5 and son on....
Substitute the given values in [1] we have;
[tex]a_n = 4+(n-1)5[/tex]
⇒[tex]a_n = 4+5n-5 = 5n-1[/tex]
⇒[tex]a_n = 5n-1[/tex]
We have to find the 100th term in the given sequence.
For n= 100
[tex]a_{100} = 5(100)-1=500-1 =499[/tex]
⇒[tex]a_{100} = 499[/tex]
Therefore, an expression to describe a rule of the sequence is, [tex]a_n = 5n-1[/tex] and the 100th term in the sequence is 499
