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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 407 · 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 10? (a) 45 (b) 55 (c) 110 (d) 50
  2. 2.Which term of the AP 17, 20, 23, 26, … is 50? (a) 14th (b) 12th (c) 11th (d) 13th
  3. 3.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 400 (b) 210 (c) 39 (d) 420
  4. 4.What is the sum of all the whole numbers from 1 to 21? (a) 232 (b) 231 (c) 210 (d) 462
  5. 5.What is the sum of all the whole numbers from 1 to 53? (a) 1432 (b) 1378 (c) 2862 (d) 1431
  6. 6.What is the sum of the first 11 terms of the AP 3, 9, 15, …? (a) 396 (b) 363 (c) 63 (d) 726
  7. 7.What is the 10th term of the AP 11, 15, 19, 23, …? (a) 36 (b) 47 (c) 51 (d) 40
  8. 8.What is the 17th term of the AP 10, 13, 16, 19, …? (a) 48 (b) 61 (c) 58 (d) 51
  9. 9.What is the sum of all the whole numbers from 1 to 66? (a) 2178 (b) 2211 (c) 2145 (d) 4422
  10. 10.What is the missing term in the AP 1, 5, ?, 13, 17? (a) 13 (b) 9 (c) 8 (d) 10
  11. 11.What is the missing term in the AP 17, 19, ?, 23, 25? (a) 23 (b) 21 (c) 20 (d) 22
  12. 12.What is the 16th term of the AP 4, 6, 8, 10, …? (a) 30 (b) 32 (c) 36 (d) 34
  13. 13.What is the missing term in the AP 18, ?, 30, 36, 42? (a) 25 (b) 24 (c) 30 (d) 23
  14. 14.What is the sum of the first 11 terms of the AP 8, 13, 18, …? (a) 368 (b) 363 (c) 58 (d) 726
  15. 15.What is the 27th term of the AP 1, 5, 9, 13, …? (a) 105 (b) 108 (c) 104 (d) 109
  16. 16.What is the missing term in the AP 5, 12, 19, ?, 33? (a) 27 (b) 25 (c) 26 (d) 33
  17. 17.What is the sum of all the whole numbers from 1 to 78? (a) 3081 (b) 3042 (c) 6162 (d) 3003
  18. 18.What is the sum of the first 10 terms of the AP 2, 6, 10, …? (a) 200 (b) 38 (c) 220 (d) 400
  19. 19.What is the 13th term of the AP 9, 12, 15, 18, …? (a) 48 (b) 39 (c) 36 (d) 45
  20. 20.What is the missing term in the AP 19, 23, ?, 31, 35? (a) 27 (b) 31 (c) 28 (d) 26
  21. 21.What is the 30th term of the AP 17, 22, 27, 32, …? (a) 167 (b) 162 (c) 145 (d) 150
  22. 22.What is the missing term in the AP 7, ?, 13, 16, 19? (a) 13 (b) 11 (c) 9 (d) 10
  23. 23.What is the 17th term of the AP 20, 28, 36, 44, …? (a) 156 (b) 128 (c) 148 (d) 136
  24. 24.What is the sum of all the whole numbers from 1 to 81? (a) 6642 (b) 3322 (c) 3240 (d) 3321
  25. 25.What is the sum of the first 7 terms of the AP 8, 10, 12, …? (a) 20 (b) 196 (c) 105 (d) 98
  26. 26.What is the missing term in the AP 4, 7, ?, 13, 16? (a) 9 (b) 10 (c) 11 (d) 13
  27. 27.What is the 33rd term of the AP 1, 8, 15, 22, …? (a) 224 (b) 232 (c) 225 (d) 231
  28. 28.What is the sum of the first 10 terms of the AP 9, 11, 13, …? (a) 180 (b) 190 (c) 27 (d) 360
  29. 29.What is the missing term in the AP 7, 15, 23, ?, 39? (a) 39 (b) 30 (c) 32 (d) 31
  30. 30.What is the sum of all the whole numbers from 1 to 90? (a) 8190 (b) 4095 (c) 4050 (d) 4005
  31. 31.Which term of the AP 20, 26, 32, 38, … is 152? (a) 23rd (b) 25th (c) 22nd (d) 24th
  32. 32.What is the sum of the first 9 terms of the AP 4, 9, 14, …? (a) 44 (b) 221 (c) 432 (d) 216
  33. 33.What is the sum of all the whole numbers from 1 to 75? (a) 2775 (b) 2851 (c) 2850 (d) 5700
  34. 34.What is the missing term in the AP 5, ?, 9, 11, 13? (a) 8 (b) 7 (c) 6 (d) 9
  35. 35.What is the sum of the first 9 terms of the AP 4, 7, 10, …? (a) 147 (b) 28 (c) 144 (d) 288
  36. 36.What is the missing term in the AP 2, ?, 6, 8, 10? (a) 5 (b) 3 (c) 6 (d) 4
  37. 37.What is the 12th term of the AP 11, 18, 25, 32, …? (a) 95 (b) 88 (c) 77 (d) 84
  38. 38.What is the sum of all the whole numbers from 1 to 91? (a) 4095 (b) 4186 (c) 4187 (d) 8372
  39. 39.What is the 13th term of the AP 16, 23, 30, 37, …? (a) 100 (b) 107 (c) 84 (d) 91
  40. 40.Which term of the AP 9, 11, 13, 15, … is 27? (a) 9th (b) 12th (c) 10th (d) 11th

Answer key

  1. 55
  2. 12th
  3. 400
  4. 231
  5. 1431
  6. 363
  7. 47
  8. 58
  9. 2211
  10. 9
  11. 21
  12. 34
  13. 24
  14. 363
  15. 105
  16. 26
  17. 3081
  18. 200
  19. 45
  20. 27
  21. 162
  22. 10
  23. 148
  24. 3321
  25. 98
  26. 10
  27. 225
  28. 180
  29. 31
  30. 4095
  31. 23rd
  32. 216
  33. 2850
  34. 7
  35. 144
  36. 4
  37. 88
  38. 4186
  39. 100
  40. 10th

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