Reading the pattern fast

Some sequences come from a fixed rule like adding a constant, while others come from shapes or recurrence rules.

Arithmetic and geometric families use direct formulas such as an=a1+(n1)da_n = a_1 + (n-1)d or an=a1rn1a_n = a_1 r^{n-1}.

The preview bars make it easier to spot whether the pattern is linear, multiplicative, or faster-growing.

Good checks to run

  • Start the index at a different position to verify the pattern rule still fits.
  • Compare arithmetic versus geometric settings with the same first term to see the growth difference.
  • Use square, cube, and triangular modes when you want to connect number patterns to familiar shapes.