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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 334 · 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 sum of all the whole numbers from 1 to 44? (a) 990 (b) 968 (c) 946 (d) 1980
  2. 2.What is the 28th term of the AP 4, 12, 20, 28, …? (a) 220 (b) 216 (c) 224 (d) 228
  3. 3.What is the sum of the first 5 terms of the AP 2, 5, 8, …? (a) 14 (b) 43 (c) 40 (d) 80
  4. 4.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 441 (b) 41 (c) 231 (d) 462
  5. 5.What is the 15th term of the AP 6, 10, 14, 18, …? (a) 66 (b) 60 (c) 62 (d) 56
  6. 6.What is the 14th term of the AP 5, 10, 15, 20, …? (a) 65 (b) 75 (c) 71 (d) 70
  7. 7.What is the 22nd term of the AP 17, 26, 35, 44, …? (a) 189 (b) 215 (c) 206 (d) 198
  8. 8.What is the 19th term of the AP 11, 14, 17, 20, …? (a) 68 (b) 54 (c) 57 (d) 65
  9. 9.Which term of the AP 4, 9, 14, 19, … is 94? (a) 20th (b) 19th (c) 18th (d) 21st
  10. 10.What is the sum of all the whole numbers from 1 to 76? (a) 2850 (b) 2888 (c) 5852 (d) 2926
  11. 11.What is the 18th term of the AP 11, 18, 25, 32, …? (a) 137 (b) 119 (c) 126 (d) 130
  12. 12.What is the 29th term of the AP 4, 11, 18, 25, …? (a) 207 (b) 203 (c) 200 (d) 196
  13. 13.What is the missing term in the AP 18, 20, 22, ?, 26? (a) 23 (b) 26 (c) 25 (d) 24
  14. 14.What is the 31st term of the AP 14, 21, 28, 35, …? (a) 224 (b) 231 (c) 210 (d) 217
  15. 15.What is the sum of the first 6 terms of the AP 9, 10, 11, …? (a) 72 (b) 69 (c) 138 (d) 14
  16. 16.What is the 20th term of the AP 2, 5, 8, 11, …? (a) 60 (b) 57 (c) 62 (d) 59
  17. 17.What is the 37th term of the AP 5, 11, 17, 23, …? (a) 216 (b) 222 (c) 221 (d) 227
  18. 18.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 289 (b) 306 (c) 153 (d) 33
  19. 19.What is the 19th term of the AP 2, 10, 18, 26, …? (a) 154 (b) 146 (c) 152 (d) 144
  20. 20.What is the missing term in the AP 15, 17, 19, ?, 23? (a) 23 (b) 21 (c) 22 (d) 20
  21. 21.What is the missing term in the AP 12, 16, ?, 24, 28? (a) 20 (b) 19 (c) 24 (d) 21
  22. 22.Which term of the AP 5, 11, 17, 23, … is 77? (a) 13th (b) 15th (c) 14th (d) 12th
  23. 23.What is the sum of all the whole numbers from 1 to 94? (a) 4418 (b) 4371 (c) 8930 (d) 4465
  24. 24.What is the sum of the first 12 terms of the AP 3, 5, 7, …? (a) 336 (b) 25 (c) 180 (d) 168
  25. 25.What is the sum of the first 10 terms of the AP 3, 8, 13, …? (a) 48 (b) 255 (c) 280 (d) 510
  26. 26.What is the 30th term of the AP 10, 13, 16, 19, …? (a) 97 (b) 90 (c) 100 (d) 87
  27. 27.What is the 20th term of the AP 10, 15, 20, 25, …? (a) 100 (b) 105 (c) 95 (d) 110
  28. 28.What is the sum of all the whole numbers from 1 to 14? (a) 210 (b) 91 (c) 98 (d) 105
  29. 29.What is the sum of the first 5 terms of the AP 3, 4, 5, …? (a) 7 (b) 50 (c) 26 (d) 25
  30. 30.What is the sum of the first 12 terms of the AP 8, 11, 14, …? (a) 588 (b) 312 (c) 294 (d) 41
  31. 31.What is the 35th term of the AP 6, 10, 14, 18, …? (a) 136 (b) 142 (c) 140 (d) 146
  32. 32.What is the 17th term of the AP 16, 20, 24, 28, …? (a) 84 (b) 68 (c) 80 (d) 64
  33. 33.What is the sum of the first 11 terms of the AP 9, 10, 11, …? (a) 155 (b) 308 (c) 19 (d) 154
  34. 34.What is the sum of all the whole numbers from 1 to 67? (a) 4556 (b) 2211 (c) 2278 (d) 2279
  35. 35.Which term of the AP 2, 4, 6, 8, … is 52? (a) 26th (b) 27th (c) 25th (d) 28th
  36. 36.What is the 32nd term of the AP 19, 23, 27, 31, …? (a) 124 (b) 128 (c) 147 (d) 143
  37. 37.What is the missing term in the AP 10, ?, 26, 34, 42? (a) 17 (b) 19 (c) 26 (d) 18
  38. 38.What is the 20th term of the AP 8, 10, 12, 14, …? (a) 40 (b) 38 (c) 48 (d) 46
  39. 39.What is the sum of the first 6 terms of the AP 2, 8, 14, …? (a) 32 (b) 204 (c) 102 (d) 120
  40. 40.What is the sum of the first 7 terms of the AP 7, 11, 15, …? (a) 266 (b) 147 (c) 133 (d) 31

Answer key

  1. 990
  2. 220
  3. 40
  4. 441
  5. 62
  6. 70
  7. 206
  8. 65
  9. 19th
  10. 2926
  11. 130
  12. 200
  13. 24
  14. 224
  15. 69
  16. 59
  17. 221
  18. 289
  19. 146
  20. 21
  21. 20
  22. 13th
  23. 4465
  24. 168
  25. 255
  26. 97
  27. 105
  28. 105
  29. 25
  30. 294
  31. 142
  32. 80
  33. 154
  34. 2278
  35. 26th
  36. 143
  37. 18
  38. 46
  39. 102
  40. 133

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