Answer:
(a) t_n = 3n - 9
(b) t_16 = 39
Step-by-step explanation:
(a)
-3 - (-6) = -3 + 6 = 3
The common difference is 3.
t_1 = -6
t_2 = -6 + 3
t_3 = -6 + 3 + 3
t_4 = -6 + 3 + 3 + 3
t_n = -6 + 3(n - 1)
t_n = -6 + 3n - 3
t_n = -9 + 3n
t_n = 3n - 9
The formula is: t_n = 3n - 9
(b) t_16 = 3(16) - 9 = 48 - 9 = 39
an = -6 + 3(n - 1)
a(16) = 39
Explicit Formula: an = a1 + d(n - 1)
Our d (common difference) is +3
Our a1 (First term) is -6
To find a(16) (the 16th term), plug in 16 for n.
