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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 783 · 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 the first 14 odd numbers (1 + 3 + 5 + …)? (a) 27 (b) 105 (c) 210 (d) 196
  2. 2.What is the missing term in the AP 10, 16, ?, 28, 34? (a) 28 (b) 21 (c) 22 (d) 23
  3. 3.What is the 40th term of the AP 8, 13, 18, 23, …? (a) 203 (b) 200 (c) 208 (d) 195
  4. 4.What is the missing term in the AP 5, 7, ?, 11, 13? (a) 8 (b) 10 (c) 9 (d) 11
  5. 5.What is the missing term in the AP 12, ?, 26, 33, 40? (a) 26 (b) 19 (c) 20 (d) 18
  6. 6.What is the sum of all the whole numbers from 1 to 76? (a) 2926 (b) 5852 (c) 2888 (d) 2850
  7. 7.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 64 (b) 36 (c) 72 (d) 15
  8. 8.Which term of the AP 1, 8, 15, 22, … is 190? (a) 30th (b) 27th (c) 29th (d) 28th
  9. 9.What is the sum of the first 10 terms of the AP 2, 4, 6, …? (a) 120 (b) 220 (c) 20 (d) 110
  10. 10.What is the 10th term of the AP 9, 12, 15, 18, …? (a) 30 (b) 36 (c) 27 (d) 39
  11. 11.What is the 36th term of the AP 20, 24, 28, 32, …? (a) 140 (b) 144 (c) 164 (d) 160
  12. 12.Which term of the AP 12, 18, 24, 30, … is 108? (a) 16th (b) 18th (c) 17th (d) 19th
  13. 13.What is the sum of all the whole numbers from 1 to 59? (a) 1771 (b) 3540 (c) 1770 (d) 1711
  14. 14.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 870 (b) 435 (c) 841 (d) 57
  15. 15.What is the 27th term of the AP 7, 11, 15, 19, …? (a) 115 (b) 108 (c) 111 (d) 104
  16. 16.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 81 (b) 90 (c) 45 (d) 17
  17. 17.What is the missing term in the AP 19, 27, 35, ?, 51? (a) 42 (b) 51 (c) 44 (d) 43
  18. 18.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 121 (c) 132 (d) 66
  19. 19.What is the sum of all the whole numbers from 1 to 100? (a) 5000 (b) 4950 (c) 5050 (d) 10100
  20. 20.What is the 36th term of the AP 10, 17, 24, 31, …? (a) 255 (b) 252 (c) 262 (d) 245
  21. 21.What is the 35th term of the AP 2, 8, 14, 20, …? (a) 210 (b) 204 (c) 206 (d) 212
  22. 22.What is the 28th term of the AP 3, 9, 15, 21, …? (a) 165 (b) 162 (c) 171 (d) 168
  23. 23.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 49 (b) 325 (c) 650 (d) 625
  24. 24.What is the sum of the first 9 terms of the AP 2, 8, 14, …? (a) 468 (b) 234 (c) 261 (d) 50
  25. 25.What is the sum of all the whole numbers from 1 to 49? (a) 2450 (b) 1176 (c) 1226 (d) 1225
  26. 26.What is the sum of the first 12 terms of the AP 2, 6, 10, …? (a) 288 (b) 312 (c) 576 (d) 46
  27. 27.Which term of the AP 11, 13, 15, 17, … is 77? (a) 34th (b) 36th (c) 35th (d) 33rd
  28. 28.What is the sum of the first 9 terms of the AP 2, 3, 4, …? (a) 10 (b) 54 (c) 108 (d) 55
  29. 29.Which term of the AP 11, 19, 27, 35, … is 243? (a) 29th (b) 32nd (c) 30th (d) 31st
  30. 30.What is the missing term in the AP 20, 28, 36, ?, 52? (a) 43 (b) 44 (c) 45 (d) 52
  31. 31.What is the 33rd term of the AP 10, 18, 26, 34, …? (a) 256 (b) 274 (c) 266 (d) 264
  32. 32.What is the sum of all the whole numbers from 1 to 39? (a) 781 (b) 780 (c) 741 (d) 1560
  33. 33.What is the sum of the first 12 terms of the AP 10, 14, 18, …? (a) 408 (b) 768 (c) 384 (d) 54
  34. 34.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 406 (b) 55 (c) 812 (d) 784
  35. 35.What is the missing term in the AP 16, 20, 24, ?, 32? (a) 32 (b) 29 (c) 27 (d) 28
  36. 36.What is the missing term in the AP 2, 8, ?, 20, 26? (a) 20 (b) 15 (c) 14 (d) 13
  37. 37.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 9 (b) 30 (c) 25 (d) 15
  38. 38.What is the 39th term of the AP 16, 22, 28, 34, …? (a) 250 (b) 234 (c) 228 (d) 244
  39. 39.What is the 39th term of the AP 2, 5, 8, 11, …? (a) 114 (b) 116 (c) 119 (d) 117
  40. 40.What is the missing term in the AP 6, ?, 12, 15, 18? (a) 8 (b) 9 (c) 10 (d) 12

Answer key

  1. 196
  2. 22
  3. 203
  4. 9
  5. 19
  6. 2926
  7. 64
  8. 28th
  9. 110
  10. 36
  11. 160
  12. 17th
  13. 1770
  14. 841
  15. 111
  16. 81
  17. 43
  18. 121
  19. 5050
  20. 255
  21. 206
  22. 165
  23. 625
  24. 234
  25. 1225
  26. 288
  27. 34th
  28. 54
  29. 30th
  30. 44
  31. 266
  32. 780
  33. 384
  34. 784
  35. 28
  36. 14
  37. 25
  38. 244
  39. 116
  40. 9

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