Answer:
[tex]a_{20}[/tex] = 84
Step-by-step explanation:
[tex]a_{n}[/tex] = [tex]a_{1}[/tex] + ( n - 1 )d
~~~~~~~~~~~~~
[tex]a_{5}[/tex] = [tex]a_{1}[/tex] + (5 - 1)d = 24
[tex]a_{9}[/tex] = [tex]a_{1}[/tex] + (9 - 1)d = 40
[tex]a_{1}[/tex] + 4d = 24 ........... (1)
[tex]a_{1}[/tex] + 8d = 40 ........... (2)
(2) - (1)
4d = 16 ⇒ d = 4
[tex]a_{1}[/tex] + 8(4) = 40 ⇒ [tex]a_{1}[/tex] = 8
[tex]a_{20}[/tex] = 8 + ( 20 - 1 ) × 4 = 84
