Explicit Form
Recursive Form
Find the Term
Graphs and Tables
Word Problems
100
f(n) = 64 + (n - 1)(-15)
For the explicit form sequence above, determine the common difference.
d = -15
100
f(1) = 45
f(n) = f(n - 1) + 5
For the recursive form sequence above, determine the common difference.
d = 5
100
14, 22, 30, 38, ...
Find f(10).
f(10) = 86
100
Find f(4).
f(4) = 25
100
On Monday, Mr. Neri gave his dog Murphy 5 treats. After that, for every day he does not poo on Mr. Neri's floor, he gets 2 additional treats. Assuming Murphy doesn't poo on the floor all week, how many treats will he get on Friday?
5 + 2 + 2 + 2 + 2 = 13 treats
200
f(n) = -245 + (n - 1)(3)
For the explicit form sequence above, find f(1).
f(1) = -245
200
f(1) = 45
f(n) = f(n - 1) + 5
For the recursive form sequence above, find f(1).
f(1) = 45
200
43, 55, 67, 79, ...
Find f(8).
f(8) = 127
200
What is the common difference of the sequence shown here?
d = 3
200
Mr. Neri accidentally cut his thumb making breakfast this weekend. He started with 10 units of blood in his body. He lost 0.25 units of blood every minute after that. Create a recursively defined sequence to represent Mr. Neri's blood level if n is the number of minutes since he cut his thumb.
f(1) = 10
f(n) = f(n - 1) - 0.25
300
13, 21, 29, 37, 45, ...
Give the explicit form equation that represents this sequence.
f(n) = 13 + (n - 1)(8)
300
f(1) = 26
f(n) = f(n - 1) - 7
Give the first five terms of this recursively defined sequence.
26, 19, 12, 5, -2
300
f(1) = 4
f(n) = f(n - 1) + 16
Find f(6)
f(6) = 84
300
Give the explicit definition of the sequence shown here.
f(n) = 200 + (n - 1)(-50)
300
Mr. Neri was playing Fortnite, and had 232 large ammo after his first elimination. For every opponent he eliminated after that, he used 13 of his large ammo. If Mr. Neri got 9 eliminations, how much ammo will he have left?
f(9) = 128 ammo
400
-475, -523, -571, -619, ...
Give the explicit form equation that represents this sequence.
f(n) = -475 + (n - 1)(-48)
400
234, 342, 450, 558, ...
Give the recursive definition of this sequence.
f(1) = 234
f(n) = f(n - 1) + 108
400
f(n) = 35 + (n - 1)(-19)
Find f(40).
f(40) = -706
400
What value belongs in the missing space?
f(43) = -345
400
Mr. Neri wants to save up money to buy a new golf club for an upcoming tournament. He currently has $225 saved, and he saves an additional $32 every week. If the club costs $500, and the big tournament 10 weeks away, will he be able to buy the club in time? Prove it.
f(n) = 225 + (n - 1)(32)
f(10) = $513
Yes, he can.