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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 28 · 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 29th term of the AP 3, 7, 11, 15, …? (a) 115 (b) 116 (c) 112 (d) 119
  2. 2.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 64 (c) 36 (d) 72
  3. 3.What is the 18th term of the AP 20, 27, 34, 41, …? (a) 146 (b) 139 (c) 119 (d) 126
  4. 4.What is the sum of all the whole numbers from 1 to 23? (a) 253 (b) 276 (c) 552 (d) 277
  5. 5.What is the 17th term of the AP 12, 19, 26, 33, …? (a) 112 (b) 131 (c) 124 (d) 119
  6. 6.What is the sum of the first 12 terms of the AP 9, 11, 13, …? (a) 480 (b) 240 (c) 252 (d) 31
  7. 7.What is the sum of the first 11 terms of the AP 2, 7, 12, …? (a) 297 (b) 594 (c) 52 (d) 302
  8. 8.What is the 32nd term of the AP 8, 12, 16, 20, …? (a) 124 (b) 132 (c) 136 (d) 128
  9. 9.What is the sum of all the whole numbers from 1 to 11? (a) 67 (b) 55 (c) 66 (d) 132
  10. 10.What is the sum of all the whole numbers from 1 to 55? (a) 1485 (b) 1541 (c) 3080 (d) 1540
  11. 11.What is the sum of the first 8 terms of the AP 7, 12, 17, …? (a) 392 (b) 216 (c) 196 (d) 42
  12. 12.What is the 10th term of the AP 18, 25, 32, 39, …? (a) 70 (b) 63 (c) 81 (d) 88
  13. 13.What is the sum of the first 11 terms of the AP 3, 6, 9, …? (a) 396 (b) 33 (c) 201 (d) 198
  14. 14.What is the sum of all the whole numbers from 1 to 70? (a) 2450 (b) 2485 (c) 2415 (d) 4970
  15. 15.What is the 10th term of the AP 12, 15, 18, 21, …? (a) 42 (b) 39 (c) 27 (d) 30
  16. 16.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 306 (b) 33 (c) 289 (d) 153
  17. 17.What is the sum of all the whole numbers from 1 to 99? (a) 4951 (b) 4950 (c) 9900 (d) 4851
  18. 18.Which term of the AP 10, 15, 20, 25, … is 195? (a) 37th (b) 39th (c) 40th (d) 38th
  19. 19.What is the sum of the first 5 terms of the AP 9, 14, 19, …? (a) 100 (b) 95 (c) 29 (d) 190
  20. 20.Which term of the AP 4, 9, 14, 19, … is 124? (a) 24th (b) 26th (c) 25th (d) 27th
  21. 21.What is the missing term in the AP 3, 7, ?, 15, 19? (a) 12 (b) 10 (c) 15 (d) 11
  22. 22.What is the sum of the first 10 terms of the AP 4, 7, 10, …? (a) 31 (b) 190 (c) 350 (d) 175
  23. 23.What is the missing term in the AP 12, ?, 28, 36, 44? (a) 19 (b) 20 (c) 28 (d) 21
  24. 24.What is the missing term in the AP 9, 12, ?, 18, 21? (a) 14 (b) 15 (c) 18 (d) 16
  25. 25.What is the sum of the first 11 terms of the AP 6, 7, 8, …? (a) 16 (b) 242 (c) 121 (d) 122
  26. 26.Which term of the AP 16, 20, 24, 28, … is 60? (a) 15th (b) 11th (c) 12th (d) 13th
  27. 27.What is the sum of all the whole numbers from 1 to 78? (a) 3081 (b) 3042 (c) 3003 (d) 6162
  28. 28.What is the missing term in the AP 8, ?, 22, 29, 36? (a) 14 (b) 16 (c) 15 (d) 22
  29. 29.What is the 17th term of the AP 16, 22, 28, 34, …? (a) 102 (b) 96 (c) 112 (d) 118
  30. 30.What is the sum of all the whole numbers from 1 to 36? (a) 1332 (b) 648 (c) 666 (d) 630
  31. 31.What is the 39th term of the AP 16, 25, 34, 43, …? (a) 351 (b) 358 (c) 367 (d) 342
  32. 32.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 35 (b) 171 (c) 342 (d) 324
  33. 33.Which term of the AP 15, 18, 21, 24, … is 129? (a) 43rd (b) 40th (c) 39th (d) 38th
  34. 34.Which term of the AP 3, 11, 19, 27, … is 115? (a) 16th (b) 14th (c) 15th (d) 17th
  35. 35.What is the sum of all the whole numbers from 1 to 47? (a) 1081 (b) 2256 (c) 1128 (d) 1129
  36. 36.What is the sum of the first 8 terms of the AP 6, 7, 8, …? (a) 13 (b) 76 (c) 80 (d) 152
  37. 37.What is the missing term in the AP 9, ?, 13, 15, 17? (a) 12 (b) 10 (c) 13 (d) 11
  38. 38.What is the sum of the first 12 terms of the AP 5, 10, 15, …? (a) 780 (b) 390 (c) 420 (d) 60
  39. 39.Which term of the AP 18, 25, 32, 39, … is 249? (a) 35th (b) 33rd (c) 34th (d) 36th
  40. 40.What is the 18th term of the AP 12, 14, 16, 18, …? (a) 48 (b) 36 (c) 46 (d) 34

Answer key

  1. 115
  2. 64
  3. 139
  4. 276
  5. 124
  6. 240
  7. 297
  8. 132
  9. 66
  10. 1540
  11. 196
  12. 81
  13. 198
  14. 2485
  15. 39
  16. 289
  17. 4950
  18. 38th
  19. 95
  20. 25th
  21. 11
  22. 175
  23. 20
  24. 15
  25. 121
  26. 12th
  27. 3081
  28. 15
  29. 112
  30. 666
  31. 358
  32. 324
  33. 39th
  34. 15th
  35. 1128
  36. 76
  37. 11
  38. 390
  39. 34th
  40. 46

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