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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 969 · 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 missing term in the AP 11, 20, 29, ?, 47? (a) 38 (b) 47 (c) 37 (d) 39
  2. 2.What is the sum of all the whole numbers from 1 to 55? (a) 1485 (b) 1541 (c) 1540 (d) 3080
  3. 3.What is the missing term in the AP 9, 15, 21, ?, 33? (a) 33 (b) 28 (c) 26 (d) 27
  4. 4.What is the 34th term of the AP 10, 13, 16, 19, …? (a) 102 (b) 112 (c) 99 (d) 109
  5. 5.What is the 30th term of the AP 13, 21, 29, 37, …? (a) 240 (b) 245 (c) 253 (d) 232
  6. 6.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 31 (b) 136 (c) 256 (d) 272
  7. 7.What is the sum of the first 5 terms of the AP 9, 12, 15, …? (a) 75 (b) 78 (c) 21 (d) 150
  8. 8.What is the 37th term of the AP 5, 10, 15, 20, …? (a) 186 (b) 190 (c) 180 (d) 185
  9. 9.Which term of the AP 14, 19, 24, 29, … is 119? (a) 24th (b) 23rd (c) 22nd (d) 21st
  10. 10.What is the 39th term of the AP 5, 7, 9, 11, …? (a) 83 (b) 78 (c) 76 (d) 81
  11. 11.What is the sum of the first 6 terms of the AP 3, 7, 11, …? (a) 156 (b) 23 (c) 90 (d) 78
  12. 12.What is the sum of the first 6 terms of the AP 1, 3, 5, …? (a) 72 (b) 36 (c) 42 (d) 11
  13. 13.What is the 36th term of the AP 17, 23, 29, 35, …? (a) 210 (b) 233 (c) 216 (d) 227
  14. 14.What is the 27th term of the AP 6, 10, 14, 18, …? (a) 108 (b) 110 (c) 104 (d) 114
  15. 15.What is the sum of the first 10 terms of the AP 8, 12, 16, …? (a) 520 (b) 280 (c) 44 (d) 260
  16. 16.What is the 31st term of the AP 18, 27, 36, 45, …? (a) 279 (b) 270 (c) 288 (d) 297
  17. 17.What is the sum of the first 6 terms of the AP 6, 7, 8, …? (a) 51 (b) 11 (c) 54 (d) 102
  18. 18.What is the sum of the first 6 terms of the AP 5, 6, 7, …? (a) 90 (b) 45 (c) 10 (d) 48
  19. 19.What is the 24th term of the AP 16, 19, 22, 25, …? (a) 85 (b) 88 (c) 69 (d) 72
  20. 20.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 300 (b) 47 (c) 600 (d) 576
  21. 21.What is the sum of the first 5 terms of the AP 4, 7, 10, …? (a) 50 (b) 53 (c) 16 (d) 100
  22. 22.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 132 (b) 21 (c) 121 (d) 66
  23. 23.What is the 21st term of the AP 17, 20, 23, 26, …? (a) 60 (b) 77 (c) 63 (d) 80
  24. 24.What is the 30th term of the AP 19, 26, 33, 40, …? (a) 210 (b) 222 (c) 229 (d) 203
  25. 25.Which term of the AP 15, 23, 31, 39, … is 263? (a) 33rd (b) 31st (c) 34th (d) 32nd
  26. 26.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 420 (b) 210 (c) 39 (d) 400
  27. 27.Which term of the AP 10, 15, 20, 25, … is 140? (a) 28th (b) 27th (c) 26th (d) 29th
  28. 28.What is the missing term in the AP 15, ?, 23, 27, 31? (a) 19 (b) 23 (c) 20 (d) 18
  29. 29.What is the 33rd term of the AP 13, 17, 21, 25, …? (a) 132 (b) 128 (c) 145 (d) 141
  30. 30.What is the sum of the first 7 terms of the AP 10, 14, 18, …? (a) 168 (b) 34 (c) 308 (d) 154
  31. 31.What is the missing term in the AP 9, ?, 25, 33, 41? (a) 16 (b) 18 (c) 17 (d) 25
  32. 32.What is the 25th term of the AP 9, 11, 13, 15, …? (a) 48 (b) 59 (c) 50 (d) 57
  33. 33.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 306 (b) 289 (c) 153 (d) 33
  34. 34.What is the sum of the first 11 terms of the AP 7, 10, 13, …? (a) 484 (b) 242 (c) 245 (d) 37
  35. 35.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 182 (b) 25 (c) 169 (d) 91
  36. 36.Which term of the AP 7, 10, 13, 16, … is 64? (a) 19th (b) 20th (c) 22nd (d) 21st
  37. 37.Which term of the AP 9, 16, 23, 30, … is 205? (a) 28th (b) 31st (c) 30th (d) 29th
  38. 38.What is the missing term in the AP 8, ?, 22, 29, 36? (a) 16 (b) 22 (c) 14 (d) 15
  39. 39.Which term of the AP 5, 11, 17, 23, … is 233? (a) 38th (b) 41st (c) 40th (d) 39th
  40. 40.What is the 21st term of the AP 19, 26, 33, 40, …? (a) 159 (b) 147 (c) 166 (d) 140

Answer key

  1. 38
  2. 1540
  3. 27
  4. 109
  5. 245
  6. 256
  7. 75
  8. 185
  9. 22nd
  10. 81
  11. 78
  12. 36
  13. 227
  14. 110
  15. 260
  16. 288
  17. 51
  18. 45
  19. 85
  20. 576
  21. 50
  22. 121
  23. 77
  24. 222
  25. 32nd
  26. 400
  27. 27th
  28. 19
  29. 141
  30. 154
  31. 17
  32. 57
  33. 289
  34. 242
  35. 169
  36. 20th
  37. 29th
  38. 15
  39. 39th
  40. 159

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