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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 445 · 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 97? (a) 4753 (b) 4656 (c) 4754 (d) 9506
  2. 2.What is the sum of all the whole numbers from 1 to 81? (a) 3240 (b) 6642 (c) 3321 (d) 3322
  3. 3.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 39 (b) 420 (c) 400 (d) 210
  4. 4.Which term of the AP 12, 20, 28, 36, … is 236? (a) 30th (b) 28th (c) 29th (d) 31st
  5. 5.What is the 14th term of the AP 4, 9, 14, 19, …? (a) 70 (b) 65 (c) 74 (d) 69
  6. 6.What is the sum of all the whole numbers from 1 to 45? (a) 1036 (b) 1035 (c) 2070 (d) 990
  7. 7.What is the missing term in the AP 2, ?, 16, 23, 30? (a) 10 (b) 8 (c) 9 (d) 16
  8. 8.What is the sum of all the whole numbers from 1 to 86? (a) 7482 (b) 3698 (c) 3741 (d) 3655
  9. 9.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 841 (b) 435 (c) 870 (d) 57
  10. 10.Which term of the AP 13, 16, 19, 22, … is 61? (a) 18th (b) 16th (c) 19th (d) 17th
  11. 11.What is the sum of the first 11 terms of the AP 1, 2, 3, …? (a) 11 (b) 66 (c) 67 (d) 132
  12. 12.What is the sum of all the whole numbers from 1 to 96? (a) 4560 (b) 9312 (c) 4608 (d) 4656
  13. 13.What is the sum of the first 10 terms of the AP 5, 6, 7, …? (a) 190 (b) 14 (c) 95 (d) 100
  14. 14.What is the missing term in the AP 3, ?, 15, 21, 27? (a) 10 (b) 15 (c) 9 (d) 8
  15. 15.What is the 29th term of the AP 1, 5, 9, 13, …? (a) 112 (b) 116 (c) 113 (d) 117
  16. 16.What is the sum of the first 12 terms of the AP 2, 8, 14, …? (a) 68 (b) 456 (c) 420 (d) 840
  17. 17.What is the 28th term of the AP 13, 19, 25, 31, …? (a) 181 (b) 162 (c) 175 (d) 168
  18. 18.What is the 17th term of the AP 16, 25, 34, 43, …? (a) 144 (b) 169 (c) 160 (d) 153
  19. 19.What is the sum of all the whole numbers from 1 to 52? (a) 1378 (b) 1352 (c) 1326 (d) 2756
  20. 20.What is the 18th term of the AP 19, 21, 23, 25, …? (a) 55 (b) 53 (c) 36 (d) 34
  21. 21.What is the sum of the first 7 terms of the AP 10, 13, 16, …? (a) 136 (b) 133 (c) 28 (d) 266
  22. 22.Which term of the AP 1, 3, 5, 7, … is 27? (a) 16th (b) 15th (c) 13th (d) 14th
  23. 23.Which term of the AP 8, 10, 12, 14, … is 72? (a) 36th (b) 32nd (c) 33rd (d) 34th
  24. 24.Which term of the AP 5, 13, 21, 29, … is 165? (a) 23rd (b) 22nd (c) 20th (d) 21st
  25. 25.What is the sum of the first 5 terms of the AP 5, 8, 11, …? (a) 58 (b) 55 (c) 17 (d) 110
  26. 26.What is the sum of the first 8 terms of the AP 2, 4, 6, …? (a) 80 (b) 72 (c) 16 (d) 144
  27. 27.What is the sum of the first 11 terms of the AP 9, 10, 11, …? (a) 19 (b) 155 (c) 154 (d) 308
  28. 28.What is the missing term in the AP 19, ?, 27, 31, 35? (a) 24 (b) 22 (c) 27 (d) 23
  29. 29.What is the sum of the first 5 terms of the AP 6, 7, 8, …? (a) 10 (b) 80 (c) 41 (d) 40
  30. 30.What is the sum of the first 11 terms of the AP 8, 10, 12, …? (a) 28 (b) 396 (c) 209 (d) 198
  31. 31.What is the 18th term of the AP 12, 19, 26, 33, …? (a) 126 (b) 119 (c) 131 (d) 138
  32. 32.What is the missing term in the AP 12, ?, 28, 36, 44? (a) 28 (b) 19 (c) 20 (d) 21
  33. 33.What is the 18th term of the AP 12, 16, 20, 24, …? (a) 84 (b) 68 (c) 72 (d) 80
  34. 34.What is the 10th term of the AP 16, 23, 30, 37, …? (a) 70 (b) 86 (c) 79 (d) 63
  35. 35.What is the sum of the first 10 terms of the AP 10, 14, 18, …? (a) 46 (b) 560 (c) 300 (d) 280
  36. 36.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 650 (b) 49 (c) 625 (d) 325
  37. 37.What is the sum of the first 10 terms of the AP 1, 4, 7, …? (a) 160 (b) 28 (c) 290 (d) 145
  38. 38.Which term of the AP 17, 23, 29, 35, … is 245? (a) 41st (b) 38th (c) 40th (d) 39th
  39. 39.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 361 (b) 380 (c) 37 (d) 190
  40. 40.What is the 37th term of the AP 9, 15, 21, 27, …? (a) 216 (b) 222 (c) 231 (d) 225

Answer key

  1. 4753
  2. 3321
  3. 400
  4. 29th
  5. 69
  6. 1035
  7. 9
  8. 3741
  9. 841
  10. 17th
  11. 66
  12. 4656
  13. 95
  14. 9
  15. 113
  16. 420
  17. 175
  18. 160
  19. 1378
  20. 53
  21. 133
  22. 14th
  23. 33rd
  24. 21st
  25. 55
  26. 72
  27. 154
  28. 23
  29. 40
  30. 198
  31. 131
  32. 20
  33. 80
  34. 79
  35. 280
  36. 625
  37. 145
  38. 39th
  39. 361
  40. 225

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