The terms in this sequence are 4 units apart. If [tex]a_1=-17[/tex] is the first term in the sequence, then the next few terms are obtained by adding 4 to the preceding term:
[tex]a_2=a_1+4=-13[/tex]
[tex]a_3=a_2+4=a_1+2\cdot4=-9[/tex]
[tex]a_4=a_3+4=a_1+3\cdot4=-5[/tex]
and so on, leading up to the [tex]n[/tex]th term
[tex]a_n=a_{n-1}+4=a_{n-2}+2\cdot4=\cdots=a_1+(n-1)\cdot4[/tex]
[tex]\implies a_n=-17+4(n-1)=4n-21[/tex]
Then the 75th term in the sequence is
[tex]a_{75}=4\cdot75-21=279[/tex]
