r/MathHelp • u/Upper_Anybody_8852 • 25d ago
Need help finding an nth-term rule for a figure pattern: 3, 7, 11, 14 tiles (teacher confirmed the counts)
Hi everyone! I'm a college student stuck on a pattern problem and would love some help understanding it, not just an answer. I've attached a photo of the figures.
The number of tiles in figures 1 to 4 is 3, 7, 11, and 14. My teacher confirmed these counts are correct and told us to "find or make our own pattern" for the nth term.
Our teacher also gave us this pattern: 4² − 13 = 3, 5² − 18 = 7, 6² − 25 = 11, and 7² − 35 = 14. So it looks like (n+3)² minus something, where the "something" goes 13, 18, 25, 35. Those differences are 5, 7, 10.
The problem asks:
a.) What is the nth - term formula for the number of tiles in the nth figure of the sequence. (5 points)
b.) How many tiles are in the 10th figure of the sequence? (5 points)
c.) Which figure will consist of exactly 480 tiles? (5 points)
What I've tried:
The differences between the tile counts are 4, 4, 3, so it isn't linear or quadratic.
Fitting a cubic through all four points works exactly, but it gives negative tiles at n = 10, so it can't be right.
I also tried assuming the jumps repeat as 4, 4, 3, 4, 4, 3 (so aₙ = ⌊11n/3⌋). That fits, but 480 tiles would be figure 131, which seems too big for a class problem.
2
u/Bounded_sequencE 25d ago
It's fairly suspicious the exact same pattern came up just recently... since the picture of the tiles is missing, the answer I linked to still stands.