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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 132 · 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 9 terms of the AP 7, 13, 19, …? (a) 558 (b) 55 (c) 306 (d) 279
  2. 2.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 64 (c) 72 (d) 36
  3. 3.What is the sum of the first 5 terms of the AP 9, 11, 13, …? (a) 17 (b) 70 (c) 130 (d) 65
  4. 4.What is the sum of all the whole numbers from 1 to 74? (a) 2701 (b) 2738 (c) 5550 (d) 2775
  5. 5.What is the sum of the first 6 terms of the AP 9, 10, 11, …? (a) 69 (b) 14 (c) 72 (d) 138
  6. 6.What is the sum of the first 11 terms of the AP 6, 11, 16, …? (a) 346 (b) 56 (c) 341 (d) 682
  7. 7.What is the 38th term of the AP 5, 7, 9, 11, …? (a) 81 (b) 76 (c) 79 (d) 74
  8. 8.What is the sum of all the whole numbers from 1 to 14? (a) 91 (b) 98 (c) 105 (d) 210
  9. 9.What is the 26th term of the AP 5, 7, 9, 11, …? (a) 52 (b) 55 (c) 50 (d) 57
  10. 10.What is the sum of all the whole numbers from 1 to 31? (a) 465 (b) 496 (c) 497 (d) 992
  11. 11.What is the 15th term of the AP 4, 6, 8, 10, …? (a) 30 (b) 34 (c) 28 (d) 32
  12. 12.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 812 (b) 406 (c) 55 (d) 784
  13. 13.What is the sum of the first 6 terms of the AP 6, 7, 8, …? (a) 102 (b) 54 (c) 11 (d) 51
  14. 14.Which term of the AP 13, 19, 25, 31, … is 133? (a) 23rd (b) 20th (c) 22nd (d) 21st
  15. 15.Which term of the AP 6, 12, 18, 24, … is 216? (a) 38th (b) 35th (c) 36th (d) 37th
  16. 16.What is the sum of the first 9 terms of the AP 7, 8, 9, …? (a) 15 (b) 198 (c) 99 (d) 100
  17. 17.What is the sum of all the whole numbers from 1 to 51? (a) 2652 (b) 1327 (c) 1275 (d) 1326
  18. 18.What is the missing term in the AP 13, 17, 21, ?, 29? (a) 29 (b) 26 (c) 25 (d) 24
  19. 19.What is the missing term in the AP 11, 16, 21, ?, 31? (a) 25 (b) 26 (c) 31 (d) 27
  20. 20.What is the 30th term of the AP 5, 14, 23, 32, …? (a) 270 (b) 275 (c) 266 (d) 261
  21. 21.What is the missing term in the AP 2, ?, 16, 23, 30? (a) 9 (b) 16 (c) 10 (d) 8
  22. 22.What is the missing term in the AP 20, ?, 32, 38, 44? (a) 26 (b) 32 (c) 25 (d) 27
  23. 23.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 53 (b) 378 (c) 729 (d) 756
  24. 24.What is the sum of all the whole numbers from 1 to 66? (a) 2178 (b) 4422 (c) 2211 (d) 2145
  25. 25.What is the 40th term of the AP 19, 24, 29, 34, …? (a) 214 (b) 195 (c) 200 (d) 219
  26. 26.What is the sum of the first 8 terms of the AP 5, 9, 13, …? (a) 33 (b) 168 (c) 152 (d) 304
  27. 27.What is the missing term in the AP 16, 22, ?, 34, 40? (a) 29 (b) 27 (c) 28 (d) 34
  28. 28.What is the 16th term of the AP 14, 17, 20, 23, …? (a) 45 (b) 48 (c) 62 (d) 59
  29. 29.Which term of the AP 2, 11, 20, 29, … is 317? (a) 37th (b) 36th (c) 35th (d) 38th
  30. 30.What is the sum of all the whole numbers from 1 to 77? (a) 6006 (b) 3004 (c) 2926 (d) 3003
  31. 31.What is the sum of the first 5 terms of the AP 10, 14, 18, …? (a) 26 (b) 100 (c) 90 (d) 180
  32. 32.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 39 (b) 210 (c) 420 (d) 400
  33. 33.What is the 33rd term of the AP 17, 19, 21, 23, …? (a) 83 (b) 64 (c) 81 (d) 66
  34. 34.Which term of the AP 14, 21, 28, 35, … is 91? (a) 14th (b) 12th (c) 13th (d) 11th
  35. 35.What is the missing term in the AP 11, 17, 23, ?, 35? (a) 30 (b) 28 (c) 29 (d) 35
  36. 36.What is the sum of all the whole numbers from 1 to 91? (a) 4187 (b) 8372 (c) 4095 (d) 4186
  37. 37.Which term of the AP 9, 14, 19, 24, … is 49? (a) 8th (b) 10th (c) 9th (d) 11th
  38. 38.What is the sum of all the whole numbers from 1 to 34? (a) 561 (b) 1190 (c) 578 (d) 595
  39. 39.What is the missing term in the AP 19, ?, 33, 40, 47? (a) 25 (b) 27 (c) 26 (d) 33
  40. 40.What is the sum of all the whole numbers from 1 to 17? (a) 306 (b) 154 (c) 136 (d) 153

Answer key

  1. 279
  2. 64
  3. 65
  4. 2775
  5. 69
  6. 341
  7. 79
  8. 105
  9. 55
  10. 496
  11. 32
  12. 784
  13. 51
  14. 21st
  15. 36th
  16. 99
  17. 1326
  18. 25
  19. 26
  20. 266
  21. 9
  22. 26
  23. 729
  24. 2211
  25. 214
  26. 152
  27. 28
  28. 59
  29. 36th
  30. 3003
  31. 90
  32. 400
  33. 81
  34. 12th
  35. 29
  36. 4186
  37. 9th
  38. 595
  39. 26
  40. 153

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