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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 790 · 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, 2, 3, …? (a) 5 (b) 30 (c) 15 (d) 16
  2. 2.What is the sum of the first 6 terms of the AP 4, 9, 14, …? (a) 114 (b) 99 (c) 29 (d) 198
  3. 3.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 91 (b) 182 (c) 169 (d) 25
  4. 4.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 870 (b) 57 (c) 435 (d) 841
  5. 5.Which term of the AP 6, 15, 24, 33, … is 123? (a) 15th (b) 14th (c) 16th (d) 13th
  6. 6.What is the 39th term of the AP 9, 11, 13, 15, …? (a) 78 (b) 76 (c) 85 (d) 87
  7. 7.What is the 21st term of the AP 4, 6, 8, 10, …? (a) 44 (b) 46 (c) 42 (d) 40
  8. 8.What is the sum of the first 12 terms of the AP 1, 7, 13, …? (a) 444 (b) 408 (c) 67 (d) 816
  9. 9.What is the sum of the first 12 terms of the AP 5, 9, 13, …? (a) 324 (b) 348 (c) 648 (d) 49
  10. 10.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 11 (b) 21 (c) 36 (d) 42
  11. 11.What is the sum of all the whole numbers from 1 to 13? (a) 91 (b) 182 (c) 92 (d) 78
  12. 12.What is the 19th term of the AP 15, 22, 29, 36, …? (a) 133 (b) 148 (c) 141 (d) 126
  13. 13.What is the sum of the first 9 terms of the AP 7, 11, 15, …? (a) 39 (b) 225 (c) 207 (d) 414
  14. 14.What is the missing term in the AP 17, 19, 21, ?, 25? (a) 24 (b) 22 (c) 23 (d) 25
  15. 15.What is the 25th term of the AP 9, 11, 13, 15, …? (a) 59 (b) 50 (c) 57 (d) 48
  16. 16.What is the 38th term of the AP 9, 16, 23, 30, …? (a) 259 (b) 266 (c) 268 (d) 275
  17. 17.What is the sum of the first 5 terms of the AP 3, 5, 7, …? (a) 35 (b) 70 (c) 40 (d) 11
  18. 18.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 380 (b) 190 (c) 361 (d) 37
  19. 19.What is the missing term in the AP 1, 3, ?, 7, 9? (a) 7 (b) 5 (c) 6 (d) 4
  20. 20.Which term of the AP 6, 10, 14, 18, … is 142? (a) 36th (b) 34th (c) 37th (d) 35th
  21. 21.What is the 11th term of the AP 15, 19, 23, 27, …? (a) 59 (b) 44 (c) 55 (d) 40
  22. 22.What is the sum of the first 10 terms of the AP 10, 16, 22, …? (a) 64 (b) 370 (c) 740 (d) 400
  23. 23.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 19 (b) 110 (c) 55 (d) 100
  24. 24.What is the sum of the first 11 terms of the AP 1, 6, 11, …? (a) 291 (b) 572 (c) 286 (d) 51
  25. 25.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 196 (b) 210 (c) 27 (d) 105
  26. 26.What is the 32nd term of the AP 20, 27, 34, 41, …? (a) 224 (b) 217 (c) 244 (d) 237
  27. 27.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 342 (b) 35 (c) 171 (d) 324
  28. 28.What is the sum of the first 6 terms of the AP 6, 10, 14, …? (a) 192 (b) 108 (c) 96 (d) 26
  29. 29.What is the 18th term of the AP 13, 21, 29, 37, …? (a) 149 (b) 144 (c) 157 (d) 136
  30. 30.What is the sum of the first 11 terms of the AP 3, 5, 7, …? (a) 23 (b) 286 (c) 154 (d) 143
  31. 31.Which term of the AP 17, 22, 27, 32, … is 67? (a) 12th (b) 13th (c) 10th (d) 11th
  32. 32.What is the sum of the first 10 terms of the AP 10, 12, 14, …? (a) 380 (b) 200 (c) 190 (d) 28
  33. 33.Which term of the AP 3, 9, 15, 21, … is 183? (a) 30th (b) 33rd (c) 32nd (d) 31st
  34. 34.What is the sum of all the whole numbers from 1 to 73? (a) 2701 (b) 2702 (c) 5402 (d) 2628
  35. 35.What is the missing term in the AP 6, ?, 10, 12, 14? (a) 7 (b) 9 (c) 8 (d) 10
  36. 36.What is the sum of the first 8 terms of the AP 3, 7, 11, …? (a) 136 (b) 272 (c) 31 (d) 152
  37. 37.What is the sum of all the whole numbers from 1 to 63? (a) 1953 (b) 4032 (c) 2017 (d) 2016
  38. 38.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 462 (b) 441 (c) 231 (d) 41
  39. 39.What is the sum of all the whole numbers from 1 to 53? (a) 1432 (b) 2862 (c) 1431 (d) 1378
  40. 40.What is the 11th term of the AP 3, 6, 9, 12, …? (a) 34 (b) 30 (c) 36 (d) 33

Answer key

  1. 15
  2. 99
  3. 169
  4. 841
  5. 14th
  6. 85
  7. 44
  8. 408
  9. 324
  10. 36
  11. 91
  12. 141
  13. 207
  14. 23
  15. 57
  16. 268
  17. 35
  18. 361
  19. 5
  20. 35th
  21. 55
  22. 370
  23. 100
  24. 286
  25. 196
  26. 237
  27. 324
  28. 96
  29. 149
  30. 143
  31. 11th
  32. 190
  33. 31st
  34. 2701
  35. 8
  36. 136
  37. 2016
  38. 441
  39. 1431
  40. 33

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