Answer:
A) -18, 3, 24, 45, ... f(1) = -18, f(n) = f(n-1) + 21 for n = 2,3,4,5,...
B) 11, 33, 55, 77, ... f(1) = 11, f(n) = f(n-1) + 22 for n>1
C) -18, -108, -648, -3,888, ... f(1) = -18, f(n) = f(n-1) * 6 for n> 1
Step-by-step explanation:
-18, 3, 24, 45, ...
Let's take look at the possible difference patterns between terms:
-18 -> 3 ==> +21 or /-6
3 -> 24 ==> +21 or *8
We see we have a common pattern possible... +21
Which is confirmed from 24 to 45.
So the function will be f(1) = -18 of course
f(n) = f(n-1) + 21 for n = 2,3,4,5,...
11, 33, 55, 77, ...
Let's take a look at the possible difference patterns here again:
11 --> 33 ==> +22 or *3
33 --> 55 ==> + 22 or *5/3
Again, pattern of +22 confirmed with 55 -> 77
f(1) = 11
f(n) = f(n-1) + 22 for n>1
-18, -108, -648, -3,888, ...
Possible patterns:
-18 --> -108 ==> -90 or *6
-108 --> -648 ==> -540 or *6
Pattern of *6 confirmed with -648 and -3,888.
f(1) = -18
f(n) = f(n-1) * 6 for n > 1
