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  • Whole common ratios

Common ratio of a sequence worksheets

The common ratio is the factor a geometric sequence multiplies by each step, and it is one division away: any term over the term before it. These free printable worksheets practice that single move so the ratio is quick to find before anything else is asked.

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Ready to printCommon ratio of a sequence
Common ratio of a sequence worksheet — Whole common ratios, free printable with answer key

The answer key prints on a separate page.

What's on this sheet

For 3, 6, 12, 24 the ratio is 6 ÷ 3 = 2, and the same 2 links every other neighbouring pair — that constancy is what separates a geometric sequence from a sequence that merely grows. Dividing at two places and confirming they match is the honest check, and these short sheets leave room to do it every time rather than trusting the first pair.

Why this sheet works

The order of the division is what a child has to hold onto: later term divided by earlier term, never the reverse. Getting it backwards turns a doubling sequence into a halving one and reports ½ where the answer is 2. Every step-by-step walk here divides in the same direction so the ratio comes out the right way up.

How this one works

One question from this sheet, worked through a step at a time.

6, −24, 96, … — the common ratio

−24 ÷ 6=−4
r = −4
  1. Each term is the one before it TIMES the same number. Divide any term by the one before it: −24 ÷ 6 = −4.
  2. The same factor works for every pair, so the common ratio is −4.