A geometric sequence multiplies by the same factor every step, so its nth term is the start times the ratio raised to a power. These free printable worksheets ask for a term far enough out that multiplying it through by hand is the long way round.
Kid stuck on one? You don’t just get the sheet.
The answer key prints on a separate page.
The formula is a₁ · rⁿ⁻¹. For 3, 6, 12, … the ratio is 2, so the 8th term is 3 · 2⁷ = 3 · 128 = 384. As with the arithmetic version, the exponent is (n − 1) and not n, because the first term already sits at the start before any multiplying happens — a child who uses n multiplies one time too many. Where the combined sequences sheet mixes arithmetic and geometric work, this page stays with geometric terms so the power of the ratio is the whole focus.
The base and the ratio are both kept small so a term like 3 · 2⁷ stays a readable whole number rather than running to seven digits. That is a deliberate choice: the lesson is the pattern, not the size of the product, and a sequence whose terms are fractions is a separate sheet for when the halving is the point.
One question from this sheet, worked through a step at a time.
1, −3, 9, … — the 8th term