Sequences, series and London

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Across
  1. 5. the number of digits of the result of 1+2+3+4+5+...+1000000
  2. 9. the first term of an arithmetic sequence is -11 and the common difference is 7. The 35th term is ....
  3. 12. type of sequence where a constant quantity is added at each step
  4. 13. The name of the Giant Ferris Wheel of London
  5. 15. Name of the city where you will be living in your host families during the school trip
  6. 19. Name of the street where the British Prime Minister lives
  7. 21. The first term of an arithmetic sequence is -1 and the fifteenth term is 27 . The common difference is :
  8. 24. 3, 3, 5, 4, 4, 3, ... what comes next ?
  9. 26. Biggest and most famous abbey in London, where many British monarchs were crowned
  10. 27. Iconic drawbridge of London
  11. 31. sum of conscutive terms of a sequence
  12. 32. The castle in London where the Crown Jewels are safely protected is called the .......
  13. 33. ordered set of numerbers, often denoted {u_n}
  14. 34. The biggest Museum in London, the British equivalent of the "Louvres" is called the .....
Down
  1. 1. the number of digits of the sum of the first 100 powers of two
  2. 2. the quantity that is added at each step in an arithmetic sequence
  3. 3. Name of the train station we will be arriving at on the first day of the school trip
  4. 4. 1, 1, 2, 6, 24, 120, what is the next term in this sequence ?
  5. 6. Type of red bus seen everywhere in London
  6. 7. type of formule where the term un is expressed in terms of the previous ones
  7. 8. the quantity that is multiplied at each step in a geometric series
  8. 10. Another name for the Londonian Subway is "The ..."
  9. 11. In an arithmetic sequence, u₃ = 80 and u₁₃ = 30. Find u₆.
  10. 14. type of formula where the term u_n is expressed in terms of n
  11. 16. the sum .. . .... .... 1 to 12 of u_k
  12. 17. Name of the palace of the Royal Family in London
  13. 18. In a geometric sequence, u₁ = 2 and r = 4. Find u₅.
  14. 20. In an arithmetic sequence, u₃ = 60 and u₂₀ = −24. Find u₁₀.
  15. 22. The river flowing through London
  16. 23. Name of the current King or Queen of the U.K
  17. 25. type of sequence where a constant quantity is mutliplied to the previous term at each step
  18. 28. a letter or number written in subscript that denotes the rank of the sequence
  19. 29. a famous sequence where the next term is given by the sum of the previous two
  20. 30. the city we are traveling to in February
  21. 31. 6, 7, 9, 8, 6, 8,... what is the next term in this sequence ?