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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 647 · 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 5 terms of the AP 1, 5, 9, …? (a) 55 (b) 45 (c) 17 (d) 90
  2. 2.Which term of the AP 3, 6, 9, 12, … is 60? (a) 19th (b) 20th (c) 22nd (d) 21st
  3. 3.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 49 (b) 325 (c) 650 (d) 625
  4. 4.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 253 (b) 43 (c) 484 (d) 506
  5. 5.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 100 (b) 55 (c) 19 (d) 110
  6. 6.What is the missing term in the AP 10, ?, 22, 28, 34? (a) 15 (b) 16 (c) 17 (d) 22
  7. 7.What is the sum of the first 6 terms of the AP 2, 8, 14, …? (a) 102 (b) 204 (c) 32 (d) 120
  8. 8.What is the sum of the first 8 terms of the AP 1, 2, 3, …? (a) 72 (b) 40 (c) 36 (d) 8
  9. 9.What is the sum of the first 7 terms of the AP 10, 13, 16, …? (a) 133 (b) 266 (c) 136 (d) 28
  10. 10.What is the sum of the first 8 terms of the AP 7, 8, 9, …? (a) 14 (b) 168 (c) 84 (d) 88
  11. 11.What is the missing term in the AP 20, ?, 24, 26, 28? (a) 24 (b) 22 (c) 21 (d) 23
  12. 12.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 169 (b) 25 (c) 182 (d) 91
  13. 13.What is the sum of the first 10 terms of the AP 3, 7, 11, …? (a) 39 (b) 230 (c) 210 (d) 420
  14. 14.What is the 30th term of the AP 3, 5, 7, 9, …? (a) 58 (b) 61 (c) 63 (d) 60
  15. 15.Which term of the AP 14, 21, 28, 35, … is 252? (a) 34th (b) 35th (c) 37th (d) 36th
  16. 16.What is the missing term in the AP 5, ?, 15, 20, 25? (a) 9 (b) 10 (c) 11 (d) 15
  17. 17.What is the sum of the first 8 terms of the AP 4, 8, 12, …? (a) 288 (b) 144 (c) 160 (d) 32
  18. 18.What is the sum of the first 6 terms of the AP 5, 6, 7, …? (a) 90 (b) 48 (c) 45 (d) 10
  19. 19.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 90 (b) 45 (c) 17 (d) 81
  20. 20.What is the sum of the first 5 terms of the AP 5, 9, 13, …? (a) 21 (b) 130 (c) 65 (d) 75
  21. 21.What is the sum of the first 9 terms of the AP 1, 4, 7, …? (a) 120 (b) 25 (c) 234 (d) 117
  22. 22.What is the sum of the first 5 terms of the AP 4, 8, 12, …? (a) 70 (b) 60 (c) 120 (d) 20
  23. 23.What is the 11th term of the AP 12, 14, 16, 18, …? (a) 22 (b) 20 (c) 34 (d) 32
  24. 24.What is the 38th term of the AP 12, 17, 22, 27, …? (a) 202 (b) 197 (c) 190 (d) 185
  25. 25.What is the sum of all the whole numbers from 1 to 25? (a) 650 (b) 300 (c) 326 (d) 325
  26. 26.What is the 22nd term of the AP 7, 11, 15, 19, …? (a) 88 (b) 91 (c) 84 (d) 95
  27. 27.What is the missing term in the AP 17, 19, 21, ?, 25? (a) 23 (b) 24 (c) 22 (d) 25
  28. 28.Which term of the AP 18, 20, 22, 24, … is 38? (a) 19th (b) 12th (c) 10th (d) 11th
  29. 29.What is the sum of all the whole numbers from 1 to 70? (a) 2450 (b) 2415 (c) 4970 (d) 2485
  30. 30.What is the missing term in the AP 17, 21, 25, ?, 33? (a) 30 (b) 28 (c) 29 (d) 33
  31. 31.What is the sum of the first 8 terms of the AP 2, 4, 6, …? (a) 80 (b) 72 (c) 16 (d) 144
  32. 32.What is the sum of the first 5 terms of the AP 7, 13, 19, …? (a) 95 (b) 110 (c) 190 (d) 31
  33. 33.What is the sum of all the whole numbers from 1 to 27? (a) 351 (b) 756 (c) 379 (d) 378
  34. 34.What is the 25th term of the AP 13, 19, 25, 31, …? (a) 163 (b) 144 (c) 150 (d) 157
  35. 35.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 210 (b) 400 (c) 420 (d) 39
  36. 36.What is the 15th term of the AP 6, 13, 20, 27, …? (a) 98 (b) 105 (c) 104 (d) 111
  37. 37.What is the 22nd term of the AP 11, 17, 23, 29, …? (a) 143 (b) 126 (c) 137 (d) 132
  38. 38.Which term of the AP 10, 14, 18, 22, … is 122? (a) 28th (b) 31st (c) 30th (d) 29th
  39. 39.What is the 17th term of the AP 2, 7, 12, 17, …? (a) 80 (b) 82 (c) 87 (d) 85
  40. 40.What is the sum of all the whole numbers from 1 to 66? (a) 2211 (b) 2145 (c) 2178 (d) 4422

Answer key

  1. 45
  2. 20th
  3. 625
  4. 484
  5. 100
  6. 16
  7. 102
  8. 36
  9. 133
  10. 84
  11. 22
  12. 169
  13. 210
  14. 61
  15. 35th
  16. 10
  17. 144
  18. 45
  19. 81
  20. 65
  21. 117
  22. 60
  23. 32
  24. 197
  25. 325
  26. 91
  27. 23
  28. 11th
  29. 2485
  30. 29
  31. 72
  32. 95
  33. 378
  34. 157
  35. 400
  36. 104
  37. 137
  38. 29th
  39. 82
  40. 2211

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