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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 120 · 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 all the whole numbers from 1 to 24? (a) 600 (b) 276 (c) 288 (d) 300
  2. 2.What is the sum of the first 9 terms of the AP 9, 13, 17, …? (a) 450 (b) 225 (c) 41 (d) 243
  3. 3.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 784 (b) 812 (c) 406 (d) 55
  4. 4.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 37 (b) 380 (c) 190 (d) 361
  5. 5.What is the 18th term of the AP 3, 6, 9, 12, …? (a) 54 (b) 51 (c) 57 (d) 55
  6. 6.What is the 33rd term of the AP 3, 6, 9, 12, …? (a) 102 (b) 96 (c) 100 (d) 99
  7. 7.What is the sum of the first 5 terms of the AP 9, 15, 21, …? (a) 105 (b) 33 (c) 210 (d) 120
  8. 8.What is the missing term in the AP 2, 6, ?, 14, 18? (a) 10 (b) 14 (c) 9 (d) 11
  9. 9.What is the sum of all the whole numbers from 1 to 30? (a) 930 (b) 450 (c) 435 (d) 465
  10. 10.What is the 31st term of the AP 15, 23, 31, 39, …? (a) 248 (b) 255 (c) 263 (d) 240
  11. 11.What is the 32nd term of the AP 5, 10, 15, 20, …? (a) 155 (b) 160 (c) 161 (d) 165
  12. 12.What is the sum of all the whole numbers from 1 to 44? (a) 990 (b) 1980 (c) 968 (d) 946
  13. 13.What is the sum of the first 10 terms of the AP 6, 10, 14, …? (a) 240 (b) 42 (c) 480 (d) 260
  14. 14.What is the 20th term of the AP 1, 10, 19, 28, …? (a) 181 (b) 171 (c) 180 (d) 172
  15. 15.What is the 37th term of the AP 6, 9, 12, 15, …? (a) 114 (b) 108 (c) 111 (d) 117
  16. 16.What is the sum of all the whole numbers from 1 to 72? (a) 5256 (b) 2628 (c) 2592 (d) 2556
  17. 17.What is the sum of the first 11 terms of the AP 3, 7, 11, …? (a) 506 (b) 43 (c) 253 (d) 275
  18. 18.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 240 (b) 29 (c) 225 (d) 120
  19. 19.What is the missing term in the AP 1, 9, ?, 25, 33? (a) 16 (b) 17 (c) 25 (d) 18
  20. 20.What is the sum of the first 9 terms of the AP 6, 7, 8, …? (a) 14 (b) 90 (c) 180 (d) 91
  21. 21.What is the sum of all the whole numbers from 1 to 34? (a) 595 (b) 578 (c) 1190 (d) 561
  22. 22.What is the missing term in the AP 17, 19, ?, 23, 25? (a) 22 (b) 20 (c) 23 (d) 21
  23. 23.What is the sum of the first 5 terms of the AP 6, 9, 12, …? (a) 63 (b) 18 (c) 60 (d) 120
  24. 24.What is the sum of all the whole numbers from 1 to 68? (a) 4692 (b) 2312 (c) 2346 (d) 2278
  25. 25.What is the 31st term of the AP 19, 28, 37, 46, …? (a) 270 (b) 298 (c) 289 (d) 279
  26. 26.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 30 (b) 25 (c) 9 (d) 15
  27. 27.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 49 (b) 650 (c) 325 (d) 625
  28. 28.What is the 28th term of the AP 4, 6, 8, 10, …? (a) 58 (b) 56 (c) 60 (d) 54
  29. 29.What is the missing term in the AP 12, 18, ?, 30, 36? (a) 30 (b) 25 (c) 24 (d) 23
  30. 30.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 78 (b) 144 (c) 23 (d) 156
  31. 31.What is the 31st term of the AP 3, 11, 19, 27, …? (a) 251 (b) 240 (c) 248 (d) 243
  32. 32.What is the missing term in the AP 14, ?, 32, 41, 50? (a) 32 (b) 22 (c) 23 (d) 24
  33. 33.What is the sum of all the whole numbers from 1 to 79? (a) 3160 (b) 3161 (c) 6320 (d) 3081
  34. 34.What is the missing term in the AP 10, 17, 24, ?, 38? (a) 30 (b) 32 (c) 38 (d) 31
  35. 35.What is the sum of all the whole numbers from 1 to 32? (a) 512 (b) 496 (c) 528 (d) 1056
  36. 36.What is the sum of the first 8 terms of the AP 7, 8, 9, …? (a) 14 (b) 84 (c) 88 (d) 168
  37. 37.What is the 39th term of the AP 16, 19, 22, 25, …? (a) 130 (b) 117 (c) 133 (d) 114
  38. 38.What is the missing term in the AP 14, 17, 20, ?, 26? (a) 23 (b) 22 (c) 24 (d) 26
  39. 39.Which term of the AP 13, 15, 17, 19, … is 27? (a) 7th (b) 8th (c) 9th (d) 10th
  40. 40.What is the 39th term of the AP 3, 10, 17, 24, …? (a) 266 (b) 273 (c) 276 (d) 269

Answer key

  1. 300
  2. 225
  3. 784
  4. 361
  5. 54
  6. 99
  7. 105
  8. 10
  9. 465
  10. 255
  11. 160
  12. 990
  13. 240
  14. 172
  15. 114
  16. 2628
  17. 253
  18. 225
  19. 17
  20. 90
  21. 595
  22. 21
  23. 60
  24. 2346
  25. 289
  26. 25
  27. 625
  28. 58
  29. 24
  30. 144
  31. 243
  32. 23
  33. 3160
  34. 31
  35. 528
  36. 84
  37. 130
  38. 23
  39. 8th
  40. 269

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