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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 34 · 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 missing term in the AP 17, ?, 33, 41, 49? (a) 24 (b) 33 (c) 25 (d) 26
  2. 2.What is the 19th term of the AP 14, 21, 28, 35, …? (a) 147 (b) 133 (c) 126 (d) 140
  3. 3.What is the sum of the first 5 terms of the AP 9, 15, 21, …? (a) 105 (b) 33 (c) 120 (d) 210
  4. 4.What is the missing term in the AP 12, ?, 16, 18, 20? (a) 14 (b) 13 (c) 15 (d) 16
  5. 5.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 11 (c) 36 (d) 42
  6. 6.What is the sum of all the whole numbers from 1 to 81? (a) 3240 (b) 3322 (c) 3321 (d) 6642
  7. 7.What is the sum of the first 12 terms of the AP 6, 12, 18, …? (a) 468 (b) 936 (c) 504 (d) 72
  8. 8.What is the 14th term of the AP 7, 10, 13, 16, …? (a) 49 (b) 46 (c) 39 (d) 42
  9. 9.What is the missing term in the AP 14, 18, ?, 26, 30? (a) 21 (b) 22 (c) 26 (d) 23
  10. 10.Which term of the AP 1, 8, 15, 22, … is 204? (a) 31st (b) 29th (c) 30th (d) 32nd
  11. 11.What is the sum of the first 10 terms of the AP 3, 5, 7, …? (a) 120 (b) 240 (c) 21 (d) 130
  12. 12.What is the 23rd term of the AP 4, 10, 16, 22, …? (a) 132 (b) 138 (c) 136 (d) 142
  13. 13.What is the 29th term of the AP 1, 6, 11, 16, …? (a) 145 (b) 140 (c) 141 (d) 146
  14. 14.What is the missing term in the AP 7, 15, 23, ?, 39? (a) 32 (b) 39 (c) 31 (d) 30
  15. 15.What is the sum of the first 5 terms of the AP 7, 12, 17, …? (a) 170 (b) 85 (c) 27 (d) 90
  16. 16.What is the 30th term of the AP 9, 13, 17, 21, …? (a) 125 (b) 120 (c) 129 (d) 116
  17. 17.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 29 (b) 120 (c) 225 (d) 240
  18. 18.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 64 (c) 72 (d) 15
  19. 19.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 37 (b) 380 (c) 190 (d) 361
  20. 20.Which term of the AP 7, 12, 17, 22, … is 127? (a) 24th (b) 27th (c) 25th (d) 26th
  21. 21.What is the sum of the first 8 terms of the AP 1, 7, 13, …? (a) 352 (b) 176 (c) 200 (d) 43
  22. 22.What is the sum of all the whole numbers from 1 to 58? (a) 3422 (b) 1653 (c) 1682 (d) 1711
  23. 23.What is the sum of all the whole numbers from 1 to 77? (a) 3004 (b) 3003 (c) 2926 (d) 6006
  24. 24.What is the 26th term of the AP 18, 24, 30, 36, …? (a) 156 (b) 174 (c) 150 (d) 168
  25. 25.What is the missing term in the AP 2, ?, 18, 26, 34? (a) 9 (b) 18 (c) 11 (d) 10
  26. 26.What is the sum of the first 10 terms of the AP 5, 10, 15, …? (a) 275 (b) 50 (c) 300 (d) 550
  27. 27.Which term of the AP 12, 15, 18, 21, … is 39? (a) 11th (b) 10th (c) 9th (d) 13th
  28. 28.What is the 17th term of the AP 10, 13, 16, 19, …? (a) 48 (b) 58 (c) 61 (d) 51
  29. 29.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 136 (b) 272 (c) 31 (d) 256
  30. 30.What is the sum of all the whole numbers from 1 to 52? (a) 1326 (b) 2756 (c) 1378 (d) 1352
  31. 31.What is the missing term in the AP 1, ?, 17, 25, 33? (a) 17 (b) 10 (c) 9 (d) 8
  32. 32.What is the sum of the first 7 terms of the AP 9, 12, 15, …? (a) 252 (b) 27 (c) 129 (d) 126
  33. 33.What is the sum of the first 7 terms of the AP 1, 6, 11, …? (a) 224 (b) 31 (c) 112 (d) 117
  34. 34.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 784 (b) 406 (c) 812 (d) 55
  35. 35.What is the sum of all the whole numbers from 1 to 45? (a) 2070 (b) 1036 (c) 990 (d) 1035
  36. 36.What is the 29th term of the AP 9, 18, 27, 36, …? (a) 262 (b) 270 (c) 252 (d) 261
  37. 37.What is the sum of the first 8 terms of the AP 5, 8, 11, …? (a) 26 (b) 136 (c) 124 (d) 248
  38. 38.What is the missing term in the AP 6, ?, 14, 18, 22? (a) 10 (b) 14 (c) 11 (d) 9
  39. 39.What is the sum of the first 8 terms of the AP 10, 12, 14, …? (a) 24 (b) 136 (c) 144 (d) 272
  40. 40.What is the sum of the first 6 terms of the AP 3, 9, 15, …? (a) 216 (b) 126 (c) 33 (d) 108

Answer key

  1. 25
  2. 140
  3. 105
  4. 14
  5. 36
  6. 3321
  7. 468
  8. 46
  9. 22
  10. 30th
  11. 120
  12. 136
  13. 141
  14. 31
  15. 85
  16. 125
  17. 225
  18. 64
  19. 361
  20. 25th
  21. 176
  22. 1711
  23. 3003
  24. 168
  25. 10
  26. 275
  27. 10th
  28. 58
  29. 256
  30. 1378
  31. 9
  32. 126
  33. 112
  34. 784
  35. 1035
  36. 261
  37. 124
  38. 10
  39. 136
  40. 108

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