Here, a = 5, d= 13-5 = 8
A(n) = 5+(n-1)8
A(n) = 5+8n-8
A(n) = 8n-3
A(100) = 8(100) - 3 = 800-3 = 797
SO OPTION B IS YOUR ANSWER,....
Answer:
Option B is correct
8n – 3;
797
Step-by-step explanation:
The nth term of an 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 consecutive terms.
n is the number of terms.
Given the sequence:
5, 13, 21, 29, 37, 45, …
This is an arithmetic sequence with first term [tex]a_1[/tex] = 5 and common difference(d) = 8
Since;
13-5 = 8,
21-13 = 8,
29-21 = 8 and so on....
We have to find the 100th term in the sequence
Substitute in [1] we have;
[tex]a_n= a_1+(100-1)d[/tex]
⇒[tex]a_n = 5+(n-1)8 = 5 +8n -8 = 8n -3[/tex]
Substitute the given values and n=100 we have;
[tex]a_{100} =800 -3= 797[/tex]
Therefore, the 100th term in the sequence is, 797 and an expression to describe a rule for the sequence is, 8n – 3;
