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1000 Science Fair Projects with Complete Instructions

Geometric Sequences

Geometric Sequences is a pattern where each number is made by multiplying the last one by the same amount.

Think of it this way

You start with one grain of rice in a bowl. Each bowl in a row holds twice as many grains as the bowl before it. The first bowl has 1 grain, the next has 2, then 4, then 8. Each step multiplies by the same number — that doubling is a geometric sequence.

Explaining geometric sequences by grade level

Pluck a guitar string, then press it at the middle and pluck again. The note jumps higher. Press at the middle of what is left and pluck once more. Each new piece is half as long. The string gets shorter by the same share each time.

Projects that explore geometric sequences

String Length and Musical Notes

On a monochord, you start with a 60 cm string and search for a single multiplier that generates all 13 half-steps in an octave. That multiplier turns out to be about 0.9439 — applied twelve times, it brings the string length from 60 cm down to 30 cm. When you move the fret to each calculated length and check the frequency with a microphone, the measured notes match the predicted ones every time. The pattern holds across three octaves, and notes one octave apart always have a 2:1 frequency ratio.

Hard