This is documentation for Mathematica 7, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.2)


gives the successive ratios of elements in list.
Ratios[list, n]
gives the n^(th) iterated ratios of list.
Ratios[list, {n1, n2, ...}]
gives the successive nk^(th) ratios at level k in a nested list.
  • Ratios divides successive elements by preceding ones, so that Ratios[{x1, x2}] gives {x2/x1}.
  • If list has length s, Ratios[list, n] has length s-n.
  • Ratios[m, {1, 0}] or Ratios[m, 1] finds the successive ratios of rows in a 2D array or matrix m. Ratios[m, {0, 1}] finds the ratios of columns.
  • Ratios[list, {n1, n2}] is equivalent to Ratios[Ratios[list, n1], {0, n2}].
First ratios:
Second ratios:
Ratios of rows, within each column:
Ratios of columns, within each row:
First ratios are constant for a geometric sequence:
FoldList with Times acts as an inverse of Ratios:
New in 7