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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 888 · 40 questions
TalentJR

How to solve it (Same step every time): In an AP the gap (common difference d) is always the same. nth term = a + (n − 1) × d, where a is the first term. Sum of n terms = n × (first + last) ÷ 2; so 1 + 2 + … + n = n × (n + 1) ÷ 2, and the first n odd numbers add up to n × n.

NameDateTime takenScore ___ / 40
  1. 1.What is the 36th term of the AP 2, 4, 6, 8, …? (a) 72 (b) 70 (c) 73 (d) 74
  2. 2.What is the missing term in the AP 2, ?, 12, 17, 22? (a) 8 (b) 6 (c) 12 (d) 7
  3. 3.What is the 32nd term of the AP 17, 19, 21, 23, …? (a) 62 (b) 81 (c) 79 (d) 64
  4. 4.What is the sum of the first 11 terms of the AP 3, 9, 15, …? (a) 363 (b) 63 (c) 396 (d) 726
  5. 5.What is the 17th term of the AP 18, 24, 30, 36, …? (a) 102 (b) 114 (c) 96 (d) 120
  6. 6.Which term of the AP 11, 20, 29, 38, … is 254? (a) 29th (b) 30th (c) 28th (d) 27th
  7. 7.What is the sum of the first 8 terms of the AP 2, 6, 10, …? (a) 128 (b) 30 (c) 144 (d) 256
  8. 8.What is the sum of the first 11 terms of the AP 6, 9, 12, …? (a) 234 (b) 462 (c) 36 (d) 231
  9. 9.What is the sum of the first 9 terms of the AP 7, 13, 19, …? (a) 279 (b) 306 (c) 55 (d) 558
  10. 10.What is the sum of the first 10 terms of the AP 6, 11, 16, …? (a) 285 (b) 310 (c) 570 (d) 51
  11. 11.Which term of the AP 4, 7, 10, 13, … is 79? (a) 26th (b) 27th (c) 28th (d) 25th
  12. 12.Which term of the AP 17, 26, 35, 44, … is 251? (a) 26th (b) 27th (c) 28th (d) 29th
  13. 13.What is the missing term in the AP 2, ?, 10, 14, 18? (a) 7 (b) 5 (c) 6 (d) 10
  14. 14.What is the 39th term of the AP 3, 9, 15, 21, …? (a) 231 (b) 228 (c) 234 (d) 237
  15. 15.Which term of the AP 19, 21, 23, 25, … is 87? (a) 35th (b) 37th (c) 34th (d) 36th
  16. 16.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 23 (b) 78 (c) 144 (d) 156
  17. 17.What is the 30th term of the AP 12, 14, 16, 18, …? (a) 58 (b) 60 (c) 70 (d) 72
  18. 18.What is the missing term in the AP 18, 22, 26, ?, 34? (a) 29 (b) 30 (c) 34 (d) 31
  19. 19.Which term of the AP 13, 18, 23, 28, … is 108? (a) 19th (b) 20th (c) 22nd (d) 21st
  20. 20.Which term of the AP 4, 8, 12, 16, … is 112? (a) 28th (b) 27th (c) 30th (d) 29th
  21. 21.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 25 (b) 169 (c) 182 (d) 91
  22. 22.What is the 32nd term of the AP 19, 27, 35, 43, …? (a) 248 (b) 256 (c) 267 (d) 275
  23. 23.What is the sum of all the whole numbers from 1 to 34? (a) 1190 (b) 595 (c) 578 (d) 561
  24. 24.What is the sum of the first 10 terms of the AP 1, 2, 3, …? (a) 60 (b) 55 (c) 110 (d) 10
  25. 25.What is the sum of all the whole numbers from 1 to 64? (a) 4160 (b) 2016 (c) 2048 (d) 2080
  26. 26.What is the sum of the first 9 terms of the AP 1, 6, 11, …? (a) 41 (b) 189 (c) 378 (d) 194
  27. 27.What is the sum of the first 8 terms of the AP 4, 9, 14, …? (a) 172 (b) 192 (c) 344 (d) 39
  28. 28.What is the sum of the first 6 terms of the AP 9, 10, 11, …? (a) 138 (b) 14 (c) 69 (d) 72
  29. 29.What is the 19th term of the AP 7, 12, 17, 22, …? (a) 90 (b) 102 (c) 95 (d) 97
  30. 30.What is the 14th term of the AP 13, 15, 17, 19, …? (a) 39 (b) 28 (c) 26 (d) 41
  31. 31.What is the sum of the first 11 terms of the AP 8, 13, 18, …? (a) 368 (b) 58 (c) 363 (d) 726
  32. 32.What is the 21st term of the AP 12, 14, 16, 18, …? (a) 40 (b) 54 (c) 52 (d) 42
  33. 33.What is the sum of the first 11 terms of the AP 6, 10, 14, …? (a) 572 (b) 46 (c) 308 (d) 286
  34. 34.What is the sum of all the whole numbers from 1 to 65? (a) 2080 (b) 2145 (c) 4290 (d) 2146
  35. 35.What is the sum of all the whole numbers from 1 to 80? (a) 3160 (b) 6480 (c) 3200 (d) 3240
  36. 36.What is the sum of the first 5 terms of the AP 3, 5, 7, …? (a) 70 (b) 40 (c) 11 (d) 35
  37. 37.What is the sum of the first 7 terms of the AP 5, 7, 9, …? (a) 154 (b) 84 (c) 77 (d) 17
  38. 38.What is the sum of the first 6 terms of the AP 3, 6, 9, …? (a) 126 (b) 63 (c) 18 (d) 72
  39. 39.Which term of the AP 19, 26, 33, 40, … is 166? (a) 21st (b) 22nd (c) 23rd (d) 24th
  40. 40.What is the 22nd term of the AP 14, 18, 22, 26, …? (a) 98 (b) 88 (c) 102 (d) 84

Answer key

  1. 72
  2. 7
  3. 79
  4. 363
  5. 114
  6. 28th
  7. 128
  8. 231
  9. 279
  10. 285
  11. 26th
  12. 27th
  13. 6
  14. 231
  15. 35th
  16. 144
  17. 70
  18. 30
  19. 20th
  20. 28th
  21. 169
  22. 267
  23. 595
  24. 55
  25. 2080
  26. 189
  27. 172
  28. 69
  29. 97
  30. 39
  31. 363
  32. 52
  33. 286
  34. 2145
  35. 3240
  36. 35
  37. 77
  38. 63
  39. 22nd
  40. 98

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