The given sequence is
[tex]-13,-15,-17,-19,\ldots[/tex]As you can notice, this sequence is about negative numbers only, also, the number is increasing in the absolute value of 2 units each time. This means its difference is -2, let's prove it
[tex]\begin{gathered} -13-2=-15 \\ -15-2=-17 \\ -17-2=-19 \end{gathered}[/tex]So, the answer to (a) is 2.
This arithmetic sequence can be defined with the following formula
[tex]a_n=a_1+(n-1)d[/tex]Where,
[tex]\begin{gathered} a_1=-13 \\ d=-2 \end{gathered}[/tex]Replacing these values, we find the equation for the sequence
[tex]\begin{gathered} a_n=-13+(n-1)(-2) \\ a_n=-13-2n+2 \\ a_n=-2n-11 \end{gathered}[/tex]Therefore, the answer so (b) is
[tex]a_n=-2n-11[/tex]At last, to find the 15th term, we just replace n=15 in the equation
[tex]a_{15}=-2(15)-11=-30-11=-41[/tex]Therefore, the answer to (c) is -41.
