Answer:
Step-by-step explanation:
Determining the expression for the sequence:
Given the sequence
10, 11, 12, 13
Here, the first element is:
a₁ = 10
An arithmetic sequence has a constant difference 'd' and is defined by
[tex]a_n=a_1+\left(n-1\right)d[/tex]
computing the differences of all the adjacent terms
[tex]11-10=1,\:\quad \:12-11=1,\:\quad \:13-12=1[/tex]
The difference between all the adjacent terms is the same and equal to
[tex]d=1[/tex]
now substituting d = 1 and a₁ = 10 in the nth term
[tex]a_n=a_1+\left(n-1\right)d[/tex]
[tex]a_n=\left(n-1\right)+10[/tex]
[tex]a_n=n+9[/tex]
Determining the value of the 9th term
Given the nth term
[tex]a_n=n+9[/tex]
substituting n = 9 to determine the 9th term
[tex]a_9=9+9[/tex]
[tex]a_9=18[/tex]
Therefore, the vale of the 9th term is:
[tex]a_9=18[/tex]
