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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 760 · 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 53? (a) 2862 (b) 1431 (c) 1432 (d) 1378
  2. 2.What is the 21st term of the AP 3, 6, 9, 12, …? (a) 60 (b) 63 (c) 64 (d) 66
  3. 3.What is the sum of the first 10 terms of the AP 1, 2, 3, …? (a) 60 (b) 10 (c) 110 (d) 55
  4. 4.What is the 21st term of the AP 20, 29, 38, 47, …? (a) 189 (b) 200 (c) 180 (d) 209
  5. 5.What is the 37th term of the AP 14, 22, 30, 38, …? (a) 296 (b) 288 (c) 310 (d) 302
  6. 6.Which term of the AP 8, 12, 16, 20, … is 124? (a) 30th (b) 31st (c) 29th (d) 32nd
  7. 7.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 90 (b) 17 (c) 81 (d) 45
  8. 8.What is the 14th term of the AP 12, 19, 26, 33, …? (a) 110 (b) 103 (c) 91 (d) 98
  9. 9.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 325 (b) 650 (c) 625 (d) 49
  10. 10.What is the 19th term of the AP 7, 10, 13, 16, …? (a) 64 (b) 61 (c) 57 (d) 54
  11. 11.What is the 12th term of the AP 17, 24, 31, 38, …? (a) 84 (b) 101 (c) 94 (d) 77
  12. 12.What is the 39th term of the AP 4, 10, 16, 22, …? (a) 228 (b) 234 (c) 232 (d) 238
  13. 13.What is the 30th term of the AP 7, 12, 17, 22, …? (a) 152 (b) 157 (c) 150 (d) 145
  14. 14.Which term of the AP 13, 15, 17, 19, … is 41? (a) 15th (b) 17th (c) 16th (d) 14th
  15. 15.What is the 14th term of the AP 6, 14, 22, 30, …? (a) 112 (b) 104 (c) 110 (d) 118
  16. 16.Which term of the AP 1, 8, 15, 22, … is 176? (a) 26th (b) 27th (c) 25th (d) 28th
  17. 17.What is the sum of the first 9 terms of the AP 3, 8, 13, …? (a) 414 (b) 207 (c) 212 (d) 43
  18. 18.What is the 40th term of the AP 2, 11, 20, 29, …? (a) 353 (b) 362 (c) 351 (d) 360
  19. 19.What is the missing term in the AP 1, 10, ?, 28, 37? (a) 28 (b) 20 (c) 18 (d) 19
  20. 20.What is the sum of all the whole numbers from 1 to 52? (a) 1352 (b) 1378 (c) 2756 (d) 1326
  21. 21.What is the 20th term of the AP 11, 13, 15, 17, …? (a) 49 (b) 38 (c) 40 (d) 51
  22. 22.What is the 22nd term of the AP 16, 20, 24, 28, …? (a) 84 (b) 88 (c) 104 (d) 100
  23. 23.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 406 (b) 784 (c) 55 (d) 812
  24. 24.What is the sum of the first 11 terms of the AP 10, 13, 16, …? (a) 550 (b) 40 (c) 275 (d) 278
  25. 25.What is the 10th term of the AP 19, 27, 35, 43, …? (a) 80 (b) 91 (c) 99 (d) 72
  26. 26.What is the sum of the first 5 terms of the AP 2, 5, 8, …? (a) 43 (b) 14 (c) 40 (d) 80
  27. 27.What is the sum of the first 5 terms of the AP 6, 11, 16, …? (a) 80 (b) 85 (c) 26 (d) 160
  28. 28.What is the sum of all the whole numbers from 1 to 27? (a) 379 (b) 351 (c) 378 (d) 756
  29. 29.What is the 40th term of the AP 12, 14, 16, 18, …? (a) 78 (b) 92 (c) 90 (d) 80
  30. 30.What is the sum of the first 8 terms of the AP 6, 9, 12, …? (a) 144 (b) 132 (c) 27 (d) 264
  31. 31.What is the missing term in the AP 16, ?, 22, 25, 28? (a) 18 (b) 22 (c) 19 (d) 20
  32. 32.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 39 (b) 400 (c) 420 (d) 210
  33. 33.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 171 (b) 35 (c) 324 (d) 342
  34. 34.What is the sum of all the whole numbers from 1 to 29? (a) 406 (b) 436 (c) 435 (d) 870
  35. 35.What is the sum of all the whole numbers from 1 to 49? (a) 1176 (b) 2450 (c) 1226 (d) 1225
  36. 36.What is the sum of the first 5 terms of the AP 5, 8, 11, …? (a) 17 (b) 110 (c) 55 (d) 58
  37. 37.What is the 10th term of the AP 19, 21, 23, 25, …? (a) 18 (b) 20 (c) 39 (d) 37
  38. 38.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 42 (b) 11 (c) 21 (d) 36
  39. 39.What is the 24th term of the AP 1, 6, 11, 16, …? (a) 121 (b) 116 (c) 115 (d) 120
  40. 40.What is the missing term in the AP 5, ?, 23, 32, 41? (a) 23 (b) 15 (c) 13 (d) 14

Answer key

  1. 1431
  2. 63
  3. 55
  4. 200
  5. 302
  6. 30th
  7. 81
  8. 103
  9. 625
  10. 61
  11. 94
  12. 232
  13. 152
  14. 15th
  15. 110
  16. 26th
  17. 207
  18. 353
  19. 19
  20. 1378
  21. 49
  22. 100
  23. 784
  24. 275
  25. 91
  26. 40
  27. 80
  28. 378
  29. 90
  30. 132
  31. 19
  32. 400
  33. 324
  34. 435
  35. 1225
  36. 55
  37. 37
  38. 36
  39. 116
  40. 14

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