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🌀 Grouped Sequences Lab

Which Group and Position
Is the Nth Number In?

1, (2,3), (4,5,6), (7,8,9,10)... is a sequence split into groups whose size grows by one each time. Set the position you want to find with the slider, and see in color exactly which group it falls in and what position it holds there.

Solving it takes two steps. ① The count of numbers up through the nth group is 1+2+...+n = n(n+1)/2. The smallest n for which this value first exceeds the position you're looking for tells you "which group" it's in. ② Subtract the count through the (n-1)th group, that is (n-1)n/2, from the position you're looking for, and you get "which position within that group."

Move the slider to pick the position you want, and check for yourself in the group diagram below exactly which group and position the calculation points to.

Overall position to find (n)20
k where k(k+1)/2 first exceeds 20
Group 6, position 5

🌀 Grouped Sequences Quiz

Question 1/3 · Correct 0