The explicit formula is:
[tex]a_n=3(-5)^n[/tex]from this we know that:
[tex]a_1=3(-5)^1=-15[/tex]now, for the second term we have:
[tex]a_2=3(-5)^2=3\cdot25=75=5\cdot15[/tex]The third term is:
[tex]a_3=3(-5)^3=3(-125)=-375=-5\cdot75[/tex]From this terms we notice that the next term will be of the form:
[tex]a_4=5\cdot375[/tex]Then the recursive formula is:
[tex]a_n=-5a_{n-1}[/tex]