[tex]\boxed { \boxed { a_n = a_1 + d(n - 1)}}[/tex]
[tex]a_{14} = -33 , a_{15} = 9,[/tex]
[tex]a_{14} = a_1 + d(14 - 1) = -33[/tex]
[tex] a_1 + 13d = -33[/tex]
[tex]a_{15} = a_1 + d(15 - 1) = 9[/tex]
[tex] a_1 + 14d = 9[/tex]
So the two equations:
[tex] a_1 + 13d = -33[/tex] ----------------- ( 1 )
[tex] a_1 + 14d = 9[/tex] ----------------- ( 2 )
(2) - (1) :
[tex]d = 42[/tex] ----------------- (Sub into 1)
[tex]a_1 + 13(42) = -33[/tex]
[tex]a_1 + 546= -33[/tex]
[tex]a_1 = -33 - 546[/tex]
[tex]a_1 = -579[/tex]
[tex]\boxed { \boxed { a_n = -578 + 42(n - 1)}}[/tex]
