Given:
The arithmetic sequence is:
10, 12, 14, 16, ...
To find:
The function that generates the given sequence if n is an integer.
Solution:
We have,
10, 12, 14, 16, ...
Here, the first term is 10 and the common difference is:
[tex]d=a_2-a_1[/tex]
[tex]d=12-10[/tex]
[tex]d=2[/tex]
The nth term of an arithmetic sequence is:
[tex]a_n=a+(n-1)d[/tex]
Where, a is the first term, d is the common difference and [tex]n\geq 1[/tex].
Putting [tex]a=10,d=2[/tex] in the above formula, we get
[tex]a_n=10+(n-1)2[/tex]
[tex]a_n=10+2n-2[/tex]
[tex]a_n=8+2n[/tex]
Therefore, the function [tex]a_n=8+2n, n\geq 1[/tex] generates the sequence.
