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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 757 · 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 the first 10 terms of the AP 10, 16, 22, …? (a) 370 (b) 740 (c) 400 (d) 64
  2. 2.What is the sum of the first 12 terms of the AP 7, 9, 11, …? (a) 228 (b) 432 (c) 29 (d) 216
  3. 3.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 289 (b) 33 (c) 306 (d) 153
  4. 4.What is the sum of all the whole numbers from 1 to 38? (a) 703 (b) 741 (c) 1482 (d) 722
  5. 5.What is the sum of the first 10 terms of the AP 4, 6, 8, …? (a) 130 (b) 140 (c) 22 (d) 260
  6. 6.Which term of the AP 1, 4, 7, 10, … is 109? (a) 36th (b) 38th (c) 39th (d) 37th
  7. 7.What is the sum of the first 12 terms of the AP 3, 5, 7, …? (a) 336 (b) 180 (c) 25 (d) 168
  8. 8.What is the sum of the first 12 terms of the AP 10, 14, 18, …? (a) 54 (b) 384 (c) 408 (d) 768
  9. 9.Which term of the AP 13, 21, 29, 37, … is 229? (a) 29th (b) 27th (c) 28th (d) 30th
  10. 10.What is the sum of the first 7 terms of the AP 5, 9, 13, …? (a) 133 (b) 119 (c) 29 (d) 238
  11. 11.What is the sum of all the whole numbers from 1 to 44? (a) 1980 (b) 990 (c) 968 (d) 946
  12. 12.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 78 (b) 144 (c) 23 (d) 156
  13. 13.What is the sum of the first 10 terms of the AP 1, 5, 9, …? (a) 210 (b) 190 (c) 37 (d) 380
  14. 14.What is the sum of the first 6 terms of the AP 1, 5, 9, …? (a) 21 (b) 66 (c) 78 (d) 132
  15. 15.What is the sum of the first 6 terms of the AP 7, 8, 9, …? (a) 60 (b) 12 (c) 114 (d) 57
  16. 16.What is the 11th term of the AP 8, 17, 26, 35, …? (a) 90 (b) 99 (c) 98 (d) 107
  17. 17.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 210 (b) 400 (c) 39 (d) 420
  18. 18.What is the 23rd term of the AP 9, 12, 15, 18, …? (a) 66 (b) 78 (c) 69 (d) 75
  19. 19.What is the 38th term of the AP 10, 15, 20, 25, …? (a) 185 (b) 200 (c) 190 (d) 195
  20. 20.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 276 (b) 45 (c) 552 (d) 529
  21. 21.What is the 21st term of the AP 14, 23, 32, 41, …? (a) 194 (b) 180 (c) 203 (d) 189
  22. 22.What is the sum of all the whole numbers from 1 to 75? (a) 2850 (b) 2775 (c) 2851 (d) 5700
  23. 23.What is the sum of the first 9 terms of the AP 9, 11, 13, …? (a) 25 (b) 162 (c) 306 (d) 153
  24. 24.What is the 12th term of the AP 2, 6, 10, 14, …? (a) 48 (b) 50 (c) 46 (d) 44
  25. 25.What is the 14th term of the AP 4, 6, 8, 10, …? (a) 30 (b) 32 (c) 28 (d) 26
  26. 26.What is the sum of the first 5 terms of the AP 4, 7, 10, …? (a) 53 (b) 16 (c) 100 (d) 50
  27. 27.What is the 15th term of the AP 11, 19, 27, 35, …? (a) 120 (b) 112 (c) 131 (d) 123
  28. 28.What is the sum of the first 8 terms of the AP 8, 12, 16, …? (a) 176 (b) 352 (c) 36 (d) 192
  29. 29.What is the sum of the first 8 terms of the AP 7, 10, 13, …? (a) 280 (b) 152 (c) 140 (d) 28
  30. 30.What is the 10th term of the AP 2, 8, 14, 20, …? (a) 56 (b) 62 (c) 54 (d) 60
  31. 31.What is the 38th term of the AP 17, 25, 33, 41, …? (a) 296 (b) 321 (c) 304 (d) 313
  32. 32.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 110 (b) 19 (c) 100 (d) 55
  33. 33.What is the missing term in the AP 17, 22, 27, ?, 37? (a) 33 (b) 31 (c) 37 (d) 32
  34. 34.What is the missing term in the AP 14, 22, 30, ?, 46? (a) 37 (b) 38 (c) 39 (d) 46
  35. 35.What is the sum of the first 10 terms of the AP 8, 13, 18, …? (a) 305 (b) 330 (c) 610 (d) 53
  36. 36.What is the 24th term of the AP 19, 22, 25, 28, …? (a) 69 (b) 72 (c) 91 (d) 88
  37. 37.What is the sum of all the whole numbers from 1 to 78? (a) 3042 (b) 6162 (c) 3003 (d) 3081
  38. 38.Which term of the AP 8, 12, 16, 20, … is 56? (a) 14th (b) 13th (c) 15th (d) 12th
  39. 39.What is the sum of the first 8 terms of the AP 10, 16, 22, …? (a) 496 (b) 272 (c) 52 (d) 248
  40. 40.What is the 26th term of the AP 7, 14, 21, 28, …? (a) 182 (b) 183 (c) 189 (d) 175

Answer key

  1. 370
  2. 216
  3. 289
  4. 741
  5. 130
  6. 37th
  7. 168
  8. 384
  9. 28th
  10. 119
  11. 990
  12. 144
  13. 190
  14. 66
  15. 57
  16. 98
  17. 400
  18. 75
  19. 195
  20. 529
  21. 194
  22. 2850
  23. 153
  24. 46
  25. 30
  26. 50
  27. 123
  28. 176
  29. 140
  30. 56
  31. 313
  32. 100
  33. 32
  34. 38
  35. 305
  36. 88
  37. 3081
  38. 13th
  39. 248
  40. 182

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