Geometric Sequences
💡 How to solve ▾
If the gaps keep growing, check for a constant ratio instead of a constant difference. Each term is the previous one multiplied by the same number.
A worked example
3, 6, 12, 24, __: each term doubles, so the next is 48.
Questions people ask
How do I tell a geometric sequence from an arithmetic one? ▾
Divide each term by the one before it. If you keep getting the same ratio, it is geometric; if the plain differences match instead, it is arithmetic.
The numbers grow really fast — any shortcut? ▾
Confirm the ratio from the first two or three terms, then just multiply the last visible term by it. You never need to rebuild the whole sequence.