Twelve sequences a sheet that grow by multiplying rather than adding - each term is two or three times the one before it. This is the pattern type where the usual method stops working: subtracting one term from the next gives a different answer every time, so a student has to notice that the numbers are being multiplied before any of it makes sense.
Six terms of tripling gets large quickly, so the first term is bounded to keep the last one under ten thousand. The blank can fall anywhere in the row, and a sequence counts as repeated when its terms match even if the gap has moved - which matters more here than elsewhere, because there are far fewer doubling and tripling sequences to draw from than there are of any other type.
Divide one term by the one before it to find the multiplier, then apply it. In 3, 9, 27, ___, 243 each term is three times the last, so the missing one is 81.
An adding pattern has the same gap between every pair of terms; this one has the same ratio. Subtracting neighbours here gives a different answer each time, which is the clue that it is multiplication.
The first term is chosen so the last stays under ten thousand, so a tripling sequence of six terms starts small - the growth does the rest.
No. Sequences are compared by their terms rather than by how the row is printed, so the same pattern cannot appear twice with the blank in a different position.