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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 109 · 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 34? (a) 578 (b) 1190 (c) 561 (d) 595
  2. 2.What is the 25th term of the AP 8, 15, 22, 29, …? (a) 168 (b) 175 (c) 176 (d) 183
  3. 3.What is the 37th term of the AP 10, 18, 26, 34, …? (a) 288 (b) 298 (c) 296 (d) 306
  4. 4.What is the sum of the first 8 terms of the AP 10, 14, 18, …? (a) 38 (b) 208 (c) 192 (d) 384
  5. 5.What is the sum of all the whole numbers from 1 to 53? (a) 1378 (b) 2862 (c) 1431 (d) 1432
  6. 6.What is the sum of the first 9 terms of the AP 1, 6, 11, …? (a) 378 (b) 194 (c) 41 (d) 189
  7. 7.What is the sum of all the whole numbers from 1 to 20? (a) 200 (b) 210 (c) 420 (d) 190
  8. 8.What is the sum of the first 10 terms of the AP 6, 11, 16, …? (a) 310 (b) 570 (c) 51 (d) 285
  9. 9.What is the sum of the first 6 terms of the AP 7, 8, 9, …? (a) 114 (b) 60 (c) 12 (d) 57
  10. 10.What is the missing term in the AP 3, 7, ?, 15, 19? (a) 10 (b) 11 (c) 15 (d) 12
  11. 11.What is the sum of all the whole numbers from 1 to 60? (a) 1770 (b) 3660 (c) 1830 (d) 1800
  12. 12.What is the missing term in the AP 16, 21, 26, ?, 36? (a) 30 (b) 36 (c) 32 (d) 31
  13. 13.Which term of the AP 1, 4, 7, 10, … is 40? (a) 14th (b) 13th (c) 15th (d) 16th
  14. 14.What is the 13th term of the AP 18, 24, 30, 36, …? (a) 72 (b) 90 (c) 96 (d) 78
  15. 15.What is the 32nd term of the AP 20, 29, 38, 47, …? (a) 308 (b) 288 (c) 299 (d) 279
  16. 16.Which term of the AP 14, 18, 22, 26, … is 170? (a) 40th (b) 41st (c) 39th (d) 42nd
  17. 17.What is the 40th term of the AP 18, 23, 28, 33, …? (a) 218 (b) 200 (c) 213 (d) 195
  18. 18.What is the missing term in the AP 15, ?, 33, 42, 51? (a) 25 (b) 24 (c) 33 (d) 23
  19. 19.Which term of the AP 19, 27, 35, 43, … is 83? (a) 9th (b) 11th (c) 8th (d) 10th
  20. 20.What is the sum of all the whole numbers from 1 to 99? (a) 9900 (b) 4851 (c) 4950 (d) 4951
  21. 21.What is the sum of the first 8 terms of the AP 1, 2, 3, …? (a) 36 (b) 8 (c) 72 (d) 40
  22. 22.What is the 37th term of the AP 8, 11, 14, 17, …? (a) 108 (b) 111 (c) 116 (d) 119
  23. 23.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 64 (c) 72 (d) 36
  24. 24.What is the 24th term of the AP 3, 10, 17, 24, …? (a) 171 (b) 164 (c) 168 (d) 161
  25. 25.Which term of the AP 19, 22, 25, 28, … is 124? (a) 35th (b) 36th (c) 37th (d) 38th
  26. 26.What is the 39th term of the AP 2, 9, 16, 23, …? (a) 268 (b) 275 (c) 266 (d) 273
  27. 27.What is the sum of all the whole numbers from 1 to 70? (a) 2450 (b) 2415 (c) 4970 (d) 2485
  28. 28.Which term of the AP 18, 27, 36, 45, … is 315? (a) 36th (b) 33rd (c) 34th (d) 35th
  29. 29.Which term of the AP 13, 17, 21, 25, … is 117? (a) 26th (b) 28th (c) 29th (d) 27th
  30. 30.What is the sum of the first 8 terms of the AP 7, 11, 15, …? (a) 35 (b) 336 (c) 184 (d) 168
  31. 31.What is the missing term in the AP 12, 17, 22, ?, 32? (a) 28 (b) 32 (c) 26 (d) 27
  32. 32.What is the sum of all the whole numbers from 1 to 17? (a) 306 (b) 136 (c) 154 (d) 153
  33. 33.Which term of the AP 2, 4, 6, 8, … is 78? (a) 41st (b) 38th (c) 40th (d) 39th
  34. 34.What is the sum of the first 6 terms of the AP 5, 8, 11, …? (a) 75 (b) 150 (c) 20 (d) 84
  35. 35.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 33 (b) 306 (c) 153 (d) 289
  36. 36.What is the sum of all the whole numbers from 1 to 33? (a) 528 (b) 1122 (c) 561 (d) 562
  37. 37.What is the 29th term of the AP 6, 10, 14, 18, …? (a) 112 (b) 116 (c) 118 (d) 122
  38. 38.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 351 (b) 676 (c) 702 (d) 51
  39. 39.What is the sum of the first 5 terms of the AP 4, 10, 16, …? (a) 160 (b) 80 (c) 28 (d) 95
  40. 40.What is the 35th term of the AP 18, 27, 36, 45, …? (a) 324 (b) 306 (c) 333 (d) 315

Answer key

  1. 595
  2. 176
  3. 298
  4. 192
  5. 1431
  6. 189
  7. 210
  8. 285
  9. 57
  10. 11
  11. 1830
  12. 31
  13. 14th
  14. 90
  15. 299
  16. 40th
  17. 213
  18. 24
  19. 9th
  20. 4950
  21. 36
  22. 116
  23. 64
  24. 164
  25. 36th
  26. 268
  27. 2485
  28. 34th
  29. 27th
  30. 168
  31. 27
  32. 153
  33. 39th
  34. 75
  35. 289
  36. 561
  37. 118
  38. 676
  39. 80
  40. 324

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