Answer:
[tex]u_{n} = -2 + (n-1)5[/tex]
Step-by-step explanation:
[tex]u_{n} = a + (n-1)d[/tex]
[tex]u_{3} = a + (3-1)d = 8[/tex]
[tex]u_{3} = a + 2d = 8[/tex]
[tex]u_{8} = a + (8-1)d = 33[/tex]
[tex]u_{8} = a + 7d = 33[/tex]
Simultaenous Equations
a + 2d = 8
a + 7d = 33
Subtract the equations
(a + 7d = 33) - (a + 2d = 8)
(a - a) + (7d - 2d) = (33 - 8)
5d = 25
d = 25/5
d = 5
Subsitute d into either equation to find a
a + 2(5) = 8
a + 10 = 8
a = 8 - 10 = -2
a = -2
a + 7(5) = 33
a + 35 = 33
a = 33 - 35 = -2
a = -2
[tex]u_{n} = -2 + (n-1)5[/tex]
