Answer:
The 19th term is 99.
Step-by-step explanation:
We can write a direct formula and use it to find the 19th term. Recall that the direct formula for an arithmetic sequence is given by:
[tex]x_n = a + d(n-1)[/tex]
Where a is the initial term and d is the common difference.
Since the first term is 9 and the common difference is 5:
[tex]\displaystyle x _ n = 9+5(n-1)[/tex]
To find the 19th term, let n = 19. Thus:
[tex]x_{19} = 9+5(19-1)[/tex]
And evaluate:
[tex]\displaystyle \begin{aligned} x_{19} &= 9+5(18) \\ &= 9+90 \\ &= 99\end{aligned}[/tex]
The 19th term is 99.
