Solution:
Given the first three terms of an arithmetic sequence as;
[tex]-5,-8,-11[/tex]
An arithmetic sequence is a sequence with a common difference d, The common difference is the difference between two consecutive terms. Where;
[tex]\begin{gathered} d=a_2-a_1 \\ \text{Where;} \\ a_2=\text{ second term;} \\ a_1=\text{first term} \end{gathered}[/tex]
Thus;
[tex]\begin{gathered} d=-8-(-5) \\ d=-8+5 \\ d=-3 \end{gathered}[/tex]
Also, the next term of the sequence can be known by adding the common difference to the previous term.
Hence, the next two terms are;
[tex]\begin{gathered} =-11+(-3) \\ =-11-3 \\ =-14 \\ \text{and } \\ =-14+(-3) \\ =-14-3 \\ =-17 \end{gathered}[/tex]
FINAL ANSWER:
[tex]-14,-17[/tex]
