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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 388 · 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 39th term of the AP 13, 17, 21, 25, …? (a) 169 (b) 152 (c) 165 (d) 156
  2. 2.What is the sum of the first 8 terms of the AP 2, 5, 8, …? (a) 200 (b) 23 (c) 112 (d) 100
  3. 3.What is the sum of all the whole numbers from 1 to 56? (a) 3192 (b) 1540 (c) 1596 (d) 1568
  4. 4.Which term of the AP 15, 21, 27, 33, … is 117? (a) 18th (b) 17th (c) 19th (d) 20th
  5. 5.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 324 (b) 342 (c) 35 (d) 171
  6. 6.What is the 16th term of the AP 6, 12, 18, 24, …? (a) 90 (b) 96 (c) 102 (d) 97
  7. 7.What is the sum of the first 10 terms of the AP 1, 3, 5, …? (a) 19 (b) 100 (c) 200 (d) 110
  8. 8.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 420 (b) 39 (c) 210 (d) 400
  9. 9.What is the 38th term of the AP 10, 16, 22, 28, …? (a) 222 (b) 238 (c) 228 (d) 232
  10. 10.What is the 25th term of the AP 10, 14, 18, 22, …? (a) 110 (b) 96 (c) 106 (d) 100
  11. 11.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 19 (b) 100 (c) 110 (d) 55
  12. 12.What is the missing term in the AP 20, 25, ?, 35, 40? (a) 30 (b) 29 (c) 31 (d) 35
  13. 13.What is the sum of all the whole numbers from 1 to 73? (a) 2701 (b) 2628 (c) 2702 (d) 5402
  14. 14.What is the sum of all the whole numbers from 1 to 29? (a) 435 (b) 870 (c) 436 (d) 406
  15. 15.What is the missing term in the AP 9, 11, ?, 15, 17? (a) 12 (b) 14 (c) 13 (d) 15
  16. 16.What is the missing term in the AP 3, 9, 15, ?, 27? (a) 27 (b) 20 (c) 21 (d) 22
  17. 17.What is the 27th term of the AP 15, 23, 31, 39, …? (a) 216 (b) 208 (c) 223 (d) 231
  18. 18.What is the 27th term of the AP 13, 16, 19, 22, …? (a) 94 (b) 81 (c) 91 (d) 78
  19. 19.What is the sum of all the whole numbers from 1 to 11? (a) 55 (b) 67 (c) 132 (d) 66
  20. 20.What is the sum of all the whole numbers from 1 to 10? (a) 50 (b) 45 (c) 55 (d) 110
  21. 21.What is the sum of the first 9 terms of the AP 3, 8, 13, …? (a) 207 (b) 212 (c) 43 (d) 414
  22. 22.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 289 (b) 33 (c) 306 (d) 153
  23. 23.Which term of the AP 3, 12, 21, 30, … is 192? (a) 22nd (b) 23rd (c) 21st (d) 24th
  24. 24.What is the sum of the first 12 terms of the AP 3, 9, 15, …? (a) 864 (b) 69 (c) 432 (d) 468
  25. 25.What is the 11th term of the AP 8, 16, 24, 32, …? (a) 96 (b) 89 (c) 88 (d) 80
  26. 26.What is the 27th term of the AP 11, 14, 17, 20, …? (a) 78 (b) 92 (c) 89 (d) 81
  27. 27.What is the sum of the first 7 terms of the AP 3, 9, 15, …? (a) 168 (b) 294 (c) 147 (d) 39
  28. 28.Which term of the AP 20, 26, 32, 38, … is 254? (a) 41st (b) 42nd (c) 39th (d) 40th
  29. 29.What is the 21st term of the AP 10, 16, 22, 28, …? (a) 130 (b) 136 (c) 120 (d) 126
  30. 30.Which term of the AP 19, 21, 23, 25, … is 79? (a) 31st (b) 32nd (c) 33rd (d) 30th
  31. 31.What is the missing term in the AP 11, ?, 17, 20, 23? (a) 13 (b) 17 (c) 14 (d) 15
  32. 32.What is the missing term in the AP 15, ?, 21, 24, 27? (a) 18 (b) 17 (c) 19 (d) 21
  33. 33.What is the sum of the first 9 terms of the AP 7, 13, 19, …? (a) 306 (b) 279 (c) 558 (d) 55
  34. 34.What is the sum of all the whole numbers from 1 to 26? (a) 325 (b) 338 (c) 702 (d) 351
  35. 35.What is the missing term in the AP 8, 17, 26, ?, 44? (a) 34 (b) 44 (c) 36 (d) 35
  36. 36.Which term of the AP 9, 17, 25, 33, … is 89? (a) 13th (b) 12th (c) 10th (d) 11th
  37. 37.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 25 (c) 30 (d) 9
  38. 38.What is the sum of the first 7 terms of the AP 3, 6, 9, …? (a) 21 (b) 87 (c) 168 (d) 84
  39. 39.What is the 29th term of the AP 2, 6, 10, 14, …? (a) 114 (b) 118 (c) 112 (d) 116
  40. 40.What is the sum of the first 11 terms of the AP 5, 8, 11, …? (a) 223 (b) 220 (c) 440 (d) 35

Answer key

  1. 165
  2. 100
  3. 1596
  4. 18th
  5. 324
  6. 96
  7. 100
  8. 400
  9. 232
  10. 106
  11. 100
  12. 30
  13. 2701
  14. 435
  15. 13
  16. 21
  17. 223
  18. 91
  19. 66
  20. 55
  21. 207
  22. 289
  23. 22nd
  24. 432
  25. 88
  26. 89
  27. 147
  28. 40th
  29. 130
  30. 31st
  31. 14
  32. 18
  33. 279
  34. 351
  35. 35
  36. 11th
  37. 25
  38. 84
  39. 114
  40. 220

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