Writing Explicit Formulas
Name _________________________A#______
Identify each sequence as either arithmetic or geometric, or neither. Then write the recursive and explicit formula for
the sequence. If the sequence is neither arithmetic nor geometric, just write the recursive formula.
1) 8, 17, 26, 35, 44, …
2) 2, 6, 18, 54, 162, …
3) -83, 16, 115, 214, 313, …
4) 9, 6, 4, ,
5) 81, 74, 67, 60, 53, …
6) 2, , 3, , 4, …
5
2
5
3
81
,
2
−
243 729
, ,
8 32
…
7
2
8) 2, 4, 7, 11, 16, …
7) 135, 45, 15, 5, , …
9) 72, -54,
8 16
,
3 9
…
10) [HONORS] 4, 16, 36, 64, 100, …
11. Jalen is doing a track workout known as a “ladder,” where he increases the distance he runs for each interval. He first
runs 100 meters, then 200 meters, then 400 meters, then 800 meters, and then finally 1600 meters.
a) Is this sequence arithmetic or geometric? Explain why.
b) Suppose Jalen runs n intervals. Write an explicit formula
to determine how far Jalen will run on the nth interval.
c) Jalen’s coach tells him that he will have to run 8 intervals using this sequence. How far will Jalen have to run on his
eighth interval? Show your work.
12. Lucas is running a similar workout where he begins by running 100 meters, then 200 meters, then 300 meters, then
400 meters, and then finally 500 meters.
a) Is Lucas’ workout an arithmetic sequence or a geometric
sequence? Explain why.
b) Write a recursive and explicit formula representing
Lucas’ workout.
c) Use the explicit formula you found in part (b) to predict how many intervals it would take for Lucas to run a mile in
one interval (mile is about 1600 meters).
13. Nigel drops a basketball from 2 meters off the ground and it bounces back up 50% of the previous height each time.
a) Assume our sequence is the height of the basketball
after each bounce. Is this sequence arithmetic or
geometric? Explain why.
b) How high will the ball bounce after the 5th bounce?
Show your work.
c) According to your explicit formula, when will the ball stop bouncing?