Solution:
The arithmetic sequence is given below as
[tex]19,24,29,34,...[/tex]Step 1:
We will calculate the common difference using the formula below
[tex]\begin{gathered} d=t_2-t_1=t_3-t_2 \\ d=24-19=29-24 \\ d=5 \end{gathered}[/tex]Step 2:
We will calculate the fifth term using the formula below
[tex]\begin{gathered} c \\ n=5,a=19,d=5 \\ t_5=19+(5-1)5 \\ t_5=19+20 \\ t_5=39 \end{gathered}[/tex]We will calculate the sixth term using the formula below
[tex]\begin{gathered} t_n=a+(n-1)d \\ n=6,a=19,d=5 \\ t_6=19+(6-1)5 \\ t_6=19+25 \\ t_6=44 \end{gathered}[/tex]We will calculate the seventh term using the formula below
[tex]\begin{gathered} t_7=a+(n-1)d \\ n=7,a=19,d=5 \\ t_7=19+(7-1)5 \\ t_7=19+30 \\ t_7=49 \end{gathered}[/tex]Hence,
The next three terms of the arithmetic sequence are given below as
[tex]\Rightarrow39,44,49[/tex]