Predicting What Comes Next: Exploring Sequences and Progressions

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Across
  1. 2. The 7th-century Indian scholar who first studied the sequence where each term is the sum of the previous two
  2. 5. A complex shape or pattern, like the branching of trees, that repeats itself at different scales
  3. 6. The specific growth pattern of a geometric progression with a common ratio of 2
  4. 8. A type of formula or rule that uses a term’s position number (n) to calculate its value directly
  5. 10. A progression where each term after the first is obtained by multiplying the previous term by a fixed number
  6. 13. A rule that gives the value of a term by relating it to the value of previous terms in the sequence
  7. 16. The geometric process used on each side of a square to construct the Sierpiński square carpet fractal
  8. 18. The mathematical name for each individual number or object found within an ordered list
  9. 19. A sequence where each term is the sum of the odd numbers up to that term, such as 1, 4, 9, 16, and 25
  10. 21. t
Down
  1. 1. A sequence (1,3,6,10,…) where each term is the sum of the natural numbers up to its position
  2. 3. The 5th-century text containing the first known written formula for the sum of the first n natural numbers
  3. 4. The small numbers used in notation like t
  4. 7. The fixed number (d) added to a term to obtain the next term in an arithmetic progression
  5. 9. The type of straight-line pattern observed when the ordered pairs of an arithmetic progression are plotted on a graph
  6. 11. A specific kind of progression where the difference between any two consecutive terms is always constant
  7. 12. An ordered list of numbers or objects where each individual member is known as a term
  8. 14. A sequence that consists of a specific, limited number of terms, such as 6, 12, 24, 48, 96
  9. 15. A type of sequence that continues without end, often represented by three dots (...)
  10. 17. match the term numbers in a sequence
  11. 19. The Polish mathematician known for his work on geometric fractals like the "triangle" and "square carpet"
  12. 20. The constant factor (r) used in a geometric progression to determine successive terms