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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 579 · 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 38th term of the AP 3, 9, 15, 21, …? (a) 225 (b) 222 (c) 231 (d) 228
  2. 2.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 19 (b) 100 (c) 110 (d) 55
  3. 3.What is the sum of the first 10 terms of the AP 2, 4, 6, …? (a) 120 (b) 20 (c) 110 (d) 220
  4. 4.What is the missing term in the AP 15, 23, ?, 39, 47? (a) 39 (b) 32 (c) 31 (d) 30
  5. 5.What is the sum of the first 9 terms of the AP 8, 13, 18, …? (a) 257 (b) 504 (c) 48 (d) 252
  6. 6.What is the 36th term of the AP 3, 12, 21, 30, …? (a) 315 (b) 318 (c) 327 (d) 324
  7. 7.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 78 (b) 23 (c) 156 (d) 144
  8. 8.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 342 (b) 324 (c) 35 (d) 171
  9. 9.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 169 (b) 182 (c) 25 (d) 91
  10. 10.What is the sum of all the whole numbers from 1 to 12? (a) 78 (b) 72 (c) 156 (d) 66
  11. 11.What is the 36th term of the AP 2, 6, 10, 14, …? (a) 140 (b) 146 (c) 144 (d) 142
  12. 12.What is the 22nd term of the AP 11, 16, 21, 26, …? (a) 116 (b) 110 (c) 121 (d) 105
  13. 13.What is the 31st term of the AP 11, 13, 15, 17, …? (a) 73 (b) 60 (c) 62 (d) 71
  14. 14.What is the 17th term of the AP 9, 18, 27, 36, …? (a) 154 (b) 144 (c) 162 (d) 153
  15. 15.What is the sum of the first 12 terms of the AP 1, 4, 7, …? (a) 228 (b) 34 (c) 210 (d) 420
  16. 16.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 72 (b) 64 (c) 36 (d) 15
  17. 17.What is the sum of the first 10 terms of the AP 7, 9, 11, …? (a) 320 (b) 160 (c) 170 (d) 25
  18. 18.What is the 26th term of the AP 3, 11, 19, 27, …? (a) 203 (b) 208 (c) 211 (d) 200
  19. 19.What is the 22nd term of the AP 6, 9, 12, 15, …? (a) 69 (b) 72 (c) 63 (d) 66
  20. 20.What is the 14th term of the AP 20, 28, 36, 44, …? (a) 104 (b) 124 (c) 132 (d) 112
  21. 21.What is the 19th term of the AP 3, 12, 21, 30, …? (a) 171 (b) 162 (c) 165 (d) 174
  22. 22.Which term of the AP 16, 18, 20, 22, … is 54? (a) 27th (b) 21st (c) 20th (d) 19th
  23. 23.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 702 (b) 676 (c) 351 (d) 51
  24. 24.What is the 22nd term of the AP 6, 14, 22, 30, …? (a) 174 (b) 168 (c) 176 (d) 182
  25. 25.Which term of the AP 11, 15, 19, 23, … is 151? (a) 38th (b) 36th (c) 35th (d) 37th
  26. 26.What is the sum of the first 7 terms of the AP 10, 12, 14, …? (a) 112 (b) 22 (c) 119 (d) 224
  27. 27.What is the 18th term of the AP 1, 7, 13, 19, …? (a) 109 (b) 102 (c) 108 (d) 103
  28. 28.What is the sum of the first 5 terms of the AP 1, 7, 13, …? (a) 130 (b) 25 (c) 80 (d) 65
  29. 29.What is the 15th term of the AP 5, 10, 15, 20, …? (a) 70 (b) 80 (c) 76 (d) 75
  30. 30.What is the sum of all the whole numbers from 1 to 13? (a) 78 (b) 92 (c) 182 (d) 91
  31. 31.What is the sum of the first 9 terms of the AP 10, 15, 20, …? (a) 540 (b) 270 (c) 275 (d) 50
  32. 32.What is the 21st term of the AP 11, 16, 21, 26, …? (a) 111 (b) 105 (c) 116 (d) 100
  33. 33.What is the 10th term of the AP 13, 22, 31, 40, …? (a) 94 (b) 103 (c) 81 (d) 90
  34. 34.What is the 39th term of the AP 8, 10, 12, 14, …? (a) 78 (b) 86 (c) 76 (d) 84
  35. 35.What is the sum of all the whole numbers from 1 to 60? (a) 3660 (b) 1830 (c) 1800 (d) 1770
  36. 36.Which term of the AP 15, 20, 25, 30, … is 60? (a) 9th (b) 12th (c) 10th (d) 11th
  37. 37.What is the 40th term of the AP 20, 22, 24, 26, …? (a) 78 (b) 100 (c) 98 (d) 80
  38. 38.What is the 23rd term of the AP 19, 22, 25, 28, …? (a) 85 (b) 88 (c) 66 (d) 69
  39. 39.What is the missing term in the AP 8, ?, 16, 20, 24? (a) 13 (b) 16 (c) 11 (d) 12
  40. 40.What is the 35th term of the AP 6, 10, 14, 18, …? (a) 140 (b) 136 (c) 146 (d) 142

Answer key

  1. 225
  2. 100
  3. 110
  4. 31
  5. 252
  6. 318
  7. 144
  8. 324
  9. 169
  10. 78
  11. 142
  12. 116
  13. 71
  14. 153
  15. 210
  16. 64
  17. 160
  18. 203
  19. 69
  20. 124
  21. 165
  22. 20th
  23. 676
  24. 174
  25. 36th
  26. 112
  27. 103
  28. 65
  29. 75
  30. 91
  31. 270
  32. 111
  33. 94
  34. 84
  35. 1830
  36. 10th
  37. 98
  38. 85
  39. 12
  40. 142

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