Answer:
[tex]a_{52}[/tex] = - 394
Step-by-step explanation:
these are the terms of an arithmetic sequence with nth term
[tex]a_{n}[/tex] = [tex]a_{1}[/tex] + (n - 1)d
where d is the common difference and [tex]a_{1}[/tex] the first term
d = - 18 - (- 10) = - 10 - (- 2) = - 2 - 6 = - 8 and [tex]a_{1}[/tex] = 14, hence
[tex]a_{52}[/tex] = 14 + (51 × - 8) = 14 - 408 = - 394
