The sequence 5, -2, -9, -16... is a arithmetric sequence with the difference between a number and its succeding term is -7. The formua for getting the nth term of an arithmetric sequence is
[tex]a_n = a_1 + (n-1)d[/tex]
where [tex]a_n[/tex] is the nth term
[tex]a_1[/tex] is the first term
n is the number of terms
d is the difference
The first term in the sequence is 5. You need to find the 50th term so n is 50. The difference (d) is -7. Substituting these values in the equation, we get the final answer
[tex] a_{50} = 5 + (50-1)(-7) \\ a_{50} = -338[/tex]
The 50th term is -338.
