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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 241 · 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 32nd term of the AP 7, 10, 13, 16, …? (a) 93 (b) 103 (c) 100 (d) 96
  2. 2.What is the missing term in the AP 7, 13, ?, 25, 31? (a) 20 (b) 25 (c) 19 (d) 18
  3. 3.What is the 35th term of the AP 16, 18, 20, 22, …? (a) 86 (b) 68 (c) 70 (d) 84
  4. 4.What is the missing term in the AP 16, 18, 20, ?, 24? (a) 23 (b) 22 (c) 21 (d) 24
  5. 5.What is the 17th term of the AP 5, 7, 9, 11, …? (a) 37 (b) 39 (c) 34 (d) 32
  6. 6.What is the sum of all the whole numbers from 1 to 48? (a) 2352 (b) 1152 (c) 1176 (d) 1128
  7. 7.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 120 (b) 240 (c) 225 (d) 29
  8. 8.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 47 (b) 576 (c) 600 (d) 300
  9. 9.What is the 17th term of the AP 13, 20, 27, 34, …? (a) 125 (b) 119 (c) 112 (d) 132
  10. 10.What is the missing term in the AP 8, ?, 22, 29, 36? (a) 22 (b) 16 (c) 14 (d) 15
  11. 11.What is the sum of all the whole numbers from 1 to 91? (a) 4187 (b) 4095 (c) 4186 (d) 8372
  12. 12.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 37 (b) 190 (c) 361 (d) 380
  13. 13.What is the sum of the first 9 terms of the AP 5, 7, 9, …? (a) 21 (b) 117 (c) 234 (d) 126
  14. 14.What is the sum of the first 11 terms of the AP 5, 6, 7, …? (a) 111 (b) 15 (c) 110 (d) 220
  15. 15.What is the sum of all the whole numbers from 1 to 17? (a) 153 (b) 154 (c) 136 (d) 306
  16. 16.What is the sum of all the whole numbers from 1 to 81? (a) 3322 (b) 3321 (c) 3240 (d) 6642
  17. 17.What is the missing term in the AP 3, 11, ?, 27, 35? (a) 20 (b) 27 (c) 19 (d) 18
  18. 18.What is the 26th term of the AP 15, 24, 33, 42, …? (a) 240 (b) 234 (c) 225 (d) 249
  19. 19.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 156 (b) 78 (c) 23 (d) 144
  20. 20.What is the sum of the first 12 terms of the AP 8, 12, 16, …? (a) 360 (b) 720 (c) 384 (d) 52
  21. 21.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 110 (c) 19 (d) 100
  22. 22.What is the 28th term of the AP 16, 25, 34, 43, …? (a) 243 (b) 268 (c) 252 (d) 259
  23. 23.What is the 26th term of the AP 9, 15, 21, 27, …? (a) 159 (b) 165 (c) 150 (d) 156
  24. 24.What is the sum of the first 7 terms of the AP 3, 6, 9, …? (a) 21 (b) 87 (c) 84 (d) 168
  25. 25.What is the 26th term of the AP 17, 22, 27, 32, …? (a) 125 (b) 130 (c) 142 (d) 147
  26. 26.What is the missing term in the AP 17, 20, ?, 26, 29? (a) 26 (b) 22 (c) 24 (d) 23
  27. 27.What is the sum of the first 5 terms of the AP 9, 15, 21, …? (a) 33 (b) 105 (c) 210 (d) 120
  28. 28.Which term of the AP 9, 17, 25, 33, … is 153? (a) 21st (b) 19th (c) 18th (d) 20th
  29. 29.What is the sum of the first 8 terms of the AP 5, 8, 11, …? (a) 124 (b) 136 (c) 26 (d) 248
  30. 30.Which term of the AP 17, 19, 21, 23, … is 71? (a) 27th (b) 29th (c) 30th (d) 28th
  31. 31.What is the sum of the first 8 terms of the AP 1, 7, 13, …? (a) 200 (b) 352 (c) 43 (d) 176
  32. 32.What is the 32nd term of the AP 3, 7, 11, 15, …? (a) 127 (b) 124 (c) 131 (d) 128
  33. 33.What is the sum of the first 5 terms of the AP 1, 5, 9, …? (a) 55 (b) 90 (c) 45 (d) 17
  34. 34.What is the sum of all the whole numbers from 1 to 24? (a) 276 (b) 288 (c) 600 (d) 300
  35. 35.What is the 34th term of the AP 8, 10, 12, 14, …? (a) 74 (b) 76 (c) 68 (d) 66
  36. 36.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 552 (b) 45 (c) 276 (d) 529
  37. 37.What is the 40th term of the AP 11, 14, 17, 20, …? (a) 131 (b) 128 (c) 120 (d) 117
  38. 38.What is the sum of all the whole numbers from 1 to 33? (a) 561 (b) 528 (c) 1122 (d) 562
  39. 39.What is the 31st term of the AP 13, 16, 19, 22, …? (a) 90 (b) 93 (c) 106 (d) 103
  40. 40.What is the 19th term of the AP 17, 25, 33, 41, …? (a) 144 (b) 169 (c) 152 (d) 161

Answer key

  1. 100
  2. 19
  3. 84
  4. 22
  5. 37
  6. 1176
  7. 225
  8. 576
  9. 125
  10. 15
  11. 4186
  12. 361
  13. 117
  14. 110
  15. 153
  16. 3321
  17. 19
  18. 240
  19. 144
  20. 360
  21. 100
  22. 259
  23. 159
  24. 84
  25. 142
  26. 23
  27. 105
  28. 19th
  29. 124
  30. 28th
  31. 176
  32. 127
  33. 45
  34. 300
  35. 74
  36. 529
  37. 128
  38. 561
  39. 103
  40. 161

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