gives the successive ratios of elements in list.


gives the n^(th) iterated ratios of list.


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}].


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Basic Examples  (2)

First ratios:

Second ratios:

Scope  (3)

Ratios of rows, within each column:

Ratios of columns, within each row:

Ratios of a TimeSeries:

Properties & Relations  (2)

First ratios are constant for a geometric sequence:

FoldList with Times acts as an inverse of Ratios:

Introduced in 2008