Answer: A) 39,366 B) 61
Step-by-step explanation:
A) -2, -6, -18, -54, ....
each following term is multiplied by 3 so it is a geometric series
[tex]a_n=-2(3)^{n-1}\\\\\\a_{10}=-2(3)^{10-1}\\.\quad =-2(3)^{9}\\.\quad =-2(19,683)\\.\quad =\boxed{-39,366}[/tex]
B) 7, 9, 12, ...
each following term is +n, so it is neither arithmetic or geometric
7 + 2 = 9
9 + 3 = 12
12 + 4 = 16
16 + 5 = 21
21 + 6 = 27
27 + 7 = 34
34 + 8 = 42
42 + 9 = 51
51 + 10 = 61 The 10th term is 61
