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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 724 · 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 10 terms of the AP 1, 4, 7, …? (a) 290 (b) 28 (c) 145 (d) 160
  2. 2.What is the sum of the first 10 terms of the AP 4, 7, 10, …? (a) 190 (b) 350 (c) 175 (d) 31
  3. 3.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 153 (b) 289 (c) 306 (d) 33
  4. 4.What is the sum of the first 6 terms of the AP 10, 12, 14, …? (a) 96 (b) 20 (c) 90 (d) 180
  5. 5.What is the missing term in the AP 2, ?, 10, 14, 18? (a) 5 (b) 10 (c) 6 (d) 7
  6. 6.What is the sum of the first 8 terms of the AP 3, 5, 7, …? (a) 88 (b) 160 (c) 17 (d) 80
  7. 7.Which term of the AP 16, 19, 22, 25, … is 52? (a) 15th (b) 13th (c) 14th (d) 12th
  8. 8.What is the 15th term of the AP 8, 15, 22, 29, …? (a) 105 (b) 98 (c) 113 (d) 106
  9. 9.What is the sum of the first 7 terms of the AP 10, 13, 16, …? (a) 136 (b) 133 (c) 28 (d) 266
  10. 10.What is the sum of the first 10 terms of the AP 6, 11, 16, …? (a) 310 (b) 51 (c) 285 (d) 570
  11. 11.What is the 33rd term of the AP 17, 22, 27, 32, …? (a) 160 (b) 182 (c) 177 (d) 165
  12. 12.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 110 (b) 55 (c) 19 (d) 100
  13. 13.What is the sum of all the whole numbers from 1 to 36? (a) 1332 (b) 666 (c) 630 (d) 648
  14. 14.What is the 26th term of the AP 14, 16, 18, 20, …? (a) 66 (b) 52 (c) 64 (d) 50
  15. 15.What is the sum of all the whole numbers from 1 to 11? (a) 66 (b) 67 (c) 132 (d) 55
  16. 16.What is the 14th term of the AP 12, 20, 28, 36, …? (a) 112 (b) 124 (c) 116 (d) 104
  17. 17.What is the 15th term of the AP 16, 18, 20, 22, …? (a) 30 (b) 44 (c) 28 (d) 46
  18. 18.Which term of the AP 5, 13, 21, 29, … is 285? (a) 38th (b) 36th (c) 37th (d) 35th
  19. 19.What is the 27th term of the AP 1, 10, 19, 28, …? (a) 243 (b) 235 (c) 234 (d) 244
  20. 20.What is the missing term in the AP 13, 18, ?, 28, 33? (a) 23 (b) 24 (c) 28 (d) 22
  21. 21.What is the 16th term of the AP 20, 22, 24, 26, …? (a) 50 (b) 32 (c) 30 (d) 52
  22. 22.What is the sum of all the whole numbers from 1 to 80? (a) 6480 (b) 3200 (c) 3240 (d) 3160
  23. 23.What is the sum of the first 9 terms of the AP 2, 3, 4, …? (a) 55 (b) 108 (c) 10 (d) 54
  24. 24.What is the sum of the first 10 terms of the AP 3, 4, 5, …? (a) 80 (b) 12 (c) 150 (d) 75
  25. 25.What is the sum of the first 6 terms of the AP 1, 7, 13, …? (a) 96 (b) 31 (c) 114 (d) 192
  26. 26.What is the missing term in the AP 3, ?, 17, 24, 31? (a) 9 (b) 10 (c) 17 (d) 11
  27. 27.What is the 25th term of the AP 3, 11, 19, 27, …? (a) 195 (b) 203 (c) 192 (d) 200
  28. 28.Which term of the AP 12, 14, 16, 18, … is 30? (a) 15th (b) 11th (c) 9th (d) 10th
  29. 29.What is the 31st term of the AP 15, 19, 23, 27, …? (a) 124 (b) 139 (c) 120 (d) 135
  30. 30.What is the sum of the first 5 terms of the AP 4, 5, 6, …? (a) 8 (b) 60 (c) 30 (d) 31
  31. 31.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 64 (c) 36 (d) 72
  32. 32.Which term of the AP 4, 13, 22, 31, … is 76? (a) 10th (b) 8th (c) 11th (d) 9th
  33. 33.What is the 40th term of the AP 4, 7, 10, 13, …? (a) 124 (b) 121 (c) 120 (d) 117
  34. 34.What is the missing term in the AP 19, ?, 27, 31, 35? (a) 23 (b) 24 (c) 27 (d) 22
  35. 35.Which term of the AP 7, 15, 23, 31, … is 71? (a) 8th (b) 11th (c) 9th (d) 10th
  36. 36.What is the 30th term of the AP 11, 16, 21, 26, …? (a) 150 (b) 161 (c) 145 (d) 156
  37. 37.What is the 27th term of the AP 16, 18, 20, 22, …? (a) 68 (b) 54 (c) 70 (d) 52
  38. 38.What is the 40th term of the AP 1, 4, 7, 10, …? (a) 120 (b) 118 (c) 117 (d) 121
  39. 39.What is the 28th term of the AP 7, 11, 15, 19, …? (a) 112 (b) 115 (c) 119 (d) 108
  40. 40.What is the 12th term of the AP 9, 18, 27, 36, …? (a) 108 (b) 99 (c) 117 (d) 109

Answer key

  1. 145
  2. 175
  3. 289
  4. 90
  5. 6
  6. 80
  7. 13th
  8. 106
  9. 133
  10. 285
  11. 177
  12. 100
  13. 666
  14. 64
  15. 66
  16. 116
  17. 44
  18. 36th
  19. 235
  20. 23
  21. 50
  22. 3240
  23. 54
  24. 75
  25. 96
  26. 10
  27. 195
  28. 10th
  29. 135
  30. 30
  31. 64
  32. 9th
  33. 121
  34. 23
  35. 9th
  36. 156
  37. 68
  38. 118
  39. 115
  40. 108

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