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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 296 · 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 11th term of the AP 6, 11, 16, 21, …? (a) 56 (b) 50 (c) 55 (d) 61
  2. 2.What is the sum of the first 8 terms of the AP 4, 9, 14, …? (a) 344 (b) 172 (c) 192 (d) 39
  3. 3.What is the 17th term of the AP 8, 12, 16, 20, …? (a) 68 (b) 64 (c) 72 (d) 76
  4. 4.What is the sum of all the whole numbers from 1 to 81? (a) 3240 (b) 3321 (c) 3322 (d) 6642
  5. 5.What is the sum of all the whole numbers from 1 to 79? (a) 3161 (b) 3081 (c) 3160 (d) 6320
  6. 6.What is the sum of the first 9 terms of the AP 9, 12, 15, …? (a) 189 (b) 33 (c) 378 (d) 192
  7. 7.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 702 (b) 51 (c) 676 (d) 351
  8. 8.What is the missing term in the AP 15, 21, ?, 33, 39? (a) 28 (b) 26 (c) 33 (d) 27
  9. 9.What is the 11th term of the AP 4, 7, 10, 13, …? (a) 33 (b) 34 (c) 30 (d) 37
  10. 10.What is the 31st term of the AP 13, 21, 29, 37, …? (a) 253 (b) 248 (c) 261 (d) 240
  11. 11.Which term of the AP 18, 23, 28, 33, … is 68? (a) 12th (b) 13th (c) 11th (d) 10th
  12. 12.What is the sum of all the whole numbers from 1 to 51? (a) 1327 (b) 1275 (c) 2652 (d) 1326
  13. 13.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 30 (c) 25 (d) 9
  14. 14.Which term of the AP 6, 10, 14, 18, … is 138? (a) 35th (b) 34th (c) 33rd (d) 36th
  15. 15.What is the sum of the first 12 terms of the AP 2, 5, 8, …? (a) 35 (b) 240 (c) 222 (d) 444
  16. 16.What is the 22nd term of the AP 3, 12, 21, 30, …? (a) 198 (b) 201 (c) 192 (d) 189
  17. 17.What is the 29th term of the AP 19, 24, 29, 34, …? (a) 140 (b) 164 (c) 145 (d) 159
  18. 18.What is the missing term in the AP 13, ?, 25, 31, 37? (a) 18 (b) 19 (c) 20 (d) 25
  19. 19.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 15 (c) 72 (d) 64
  20. 20.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 182 (b) 25 (c) 91 (d) 169
  21. 21.What is the sum of all the whole numbers from 1 to 31? (a) 465 (b) 496 (c) 497 (d) 992
  22. 22.What is the sum of the first 5 terms of the AP 1, 6, 11, …? (a) 60 (b) 55 (c) 110 (d) 21
  23. 23.What is the sum of all the whole numbers from 1 to 11? (a) 66 (b) 55 (c) 132 (d) 67
  24. 24.Which term of the AP 6, 8, 10, 12, … is 24? (a) 10th (b) 12th (c) 9th (d) 11th
  25. 25.Which term of the AP 5, 8, 11, 14, … is 101? (a) 32nd (b) 33rd (c) 34th (d) 35th
  26. 26.What is the sum of all the whole numbers from 1 to 48? (a) 1128 (b) 1152 (c) 2352 (d) 1176
  27. 27.What is the 18th term of the AP 19, 27, 35, 43, …? (a) 144 (b) 155 (c) 163 (d) 136
  28. 28.What is the sum of all the whole numbers from 1 to 40? (a) 780 (b) 820 (c) 800 (d) 1640
  29. 29.What is the sum of all the whole numbers from 1 to 44? (a) 1980 (b) 968 (c) 990 (d) 946
  30. 30.What is the sum of all the whole numbers from 1 to 89? (a) 4005 (b) 3916 (c) 8010 (d) 4006
  31. 31.Which term of the AP 15, 20, 25, 30, … is 180? (a) 35th (b) 33rd (c) 36th (d) 34th
  32. 32.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 136 (b) 31 (c) 272 (d) 256
  33. 33.What is the sum of the first 6 terms of the AP 8, 14, 20, …? (a) 138 (b) 156 (c) 276 (d) 38
  34. 34.What is the 23rd term of the AP 5, 7, 9, 11, …? (a) 51 (b) 46 (c) 44 (d) 49
  35. 35.What is the 13th term of the AP 8, 12, 16, 20, …? (a) 60 (b) 56 (c) 48 (d) 52
  36. 36.What is the sum of all the whole numbers from 1 to 80? (a) 3240 (b) 6480 (c) 3200 (d) 3160
  37. 37.What is the sum of the first 8 terms of the AP 6, 8, 10, …? (a) 104 (b) 20 (c) 112 (d) 208
  38. 38.What is the 13th term of the AP 8, 10, 12, 14, …? (a) 24 (b) 32 (c) 26 (d) 34
  39. 39.What is the missing term in the AP 9, 14, ?, 24, 29? (a) 19 (b) 20 (c) 24 (d) 18
  40. 40.What is the sum of the first 7 terms of the AP 1, 5, 9, …? (a) 25 (b) 91 (c) 182 (d) 105

Answer key

  1. 56
  2. 172
  3. 72
  4. 3321
  5. 3160
  6. 189
  7. 676
  8. 27
  9. 34
  10. 253
  11. 11th
  12. 1326
  13. 25
  14. 34th
  15. 222
  16. 192
  17. 159
  18. 19
  19. 64
  20. 169
  21. 496
  22. 55
  23. 66
  24. 10th
  25. 33rd
  26. 1176
  27. 155
  28. 820
  29. 990
  30. 4005
  31. 34th
  32. 256
  33. 138
  34. 49
  35. 56
  36. 3240
  37. 104
  38. 32
  39. 19
  40. 91

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