← Sequences and AP lesson New set →

Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 315 · 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 7 terms of the AP 2, 6, 10, …? (a) 196 (b) 26 (c) 98 (d) 112
  2. 2.What is the sum of the first 6 terms of the AP 6, 7, 8, …? (a) 11 (b) 54 (c) 102 (d) 51
  3. 3.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 56 (b) 13 (c) 28 (d) 49
  4. 4.What is the missing term in the AP 13, 19, ?, 31, 37? (a) 31 (b) 26 (c) 25 (d) 24
  5. 5.What is the sum of all the whole numbers from 1 to 47? (a) 1081 (b) 1129 (c) 2256 (d) 1128
  6. 6.What is the sum of all the whole numbers from 1 to 17? (a) 153 (b) 306 (c) 136 (d) 154
  7. 7.What is the missing term in the AP 1, 8, 15, ?, 29? (a) 23 (b) 22 (c) 29 (d) 21
  8. 8.What is the 39th term of the AP 1, 6, 11, 16, …? (a) 191 (b) 196 (c) 190 (d) 195
  9. 9.What is the sum of the first 8 terms of the AP 5, 9, 13, …? (a) 304 (b) 33 (c) 152 (d) 168
  10. 10.What is the sum of the first 12 terms of the AP 2, 7, 12, …? (a) 708 (b) 354 (c) 57 (d) 384
  11. 11.What is the 18th term of the AP 9, 15, 21, 27, …? (a) 108 (b) 111 (c) 102 (d) 117
  12. 12.Which term of the AP 5, 14, 23, 32, … is 167? (a) 19th (b) 21st (c) 20th (d) 18th
  13. 13.Which term of the AP 12, 14, 16, 18, … is 62? (a) 27th (b) 26th (c) 25th (d) 31st
  14. 14.What is the sum of the first 9 terms of the AP 7, 9, 11, …? (a) 270 (b) 144 (c) 135 (d) 23
  15. 15.What is the missing term in the AP 1, 9, ?, 25, 33? (a) 16 (b) 17 (c) 25 (d) 18
  16. 16.What is the sum of all the whole numbers from 1 to 53? (a) 1431 (b) 2862 (c) 1432 (d) 1378
  17. 17.What is the 22nd term of the AP 19, 24, 29, 34, …? (a) 129 (b) 105 (c) 124 (d) 110
  18. 18.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 210 (b) 196 (c) 105 (d) 27
  19. 19.What is the 33rd term of the AP 15, 17, 19, 21, …? (a) 81 (b) 79 (c) 66 (d) 64
  20. 20.What is the missing term in the AP 20, ?, 26, 29, 32? (a) 23 (b) 24 (c) 22 (d) 26
  21. 21.What is the sum of the first 6 terms of the AP 8, 11, 14, …? (a) 93 (b) 186 (c) 102 (d) 23
  22. 22.What is the sum of the first 5 terms of the AP 3, 6, 9, …? (a) 90 (b) 15 (c) 48 (d) 45
  23. 23.What is the sum of the first 10 terms of the AP 4, 5, 6, …? (a) 90 (b) 170 (c) 13 (d) 85
  24. 24.What is the sum of the first 5 terms of the AP 7, 9, 11, …? (a) 60 (b) 55 (c) 15 (d) 110
  25. 25.What is the sum of all the whole numbers from 1 to 51? (a) 2652 (b) 1275 (c) 1327 (d) 1326
  26. 26.What is the 35th term of the AP 20, 22, 24, 26, …? (a) 88 (b) 68 (c) 90 (d) 70
  27. 27.What is the missing term in the AP 4, 10, ?, 22, 28? (a) 16 (b) 22 (c) 15 (d) 17
  28. 28.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 78 (b) 23 (c) 156 (d) 144
  29. 29.What is the sum of all the whole numbers from 1 to 26? (a) 325 (b) 702 (c) 338 (d) 351
  30. 30.What is the 16th term of the AP 9, 12, 15, 18, …? (a) 45 (b) 57 (c) 54 (d) 48
  31. 31.What is the sum of the first 9 terms of the AP 4, 9, 14, …? (a) 432 (b) 44 (c) 216 (d) 221
  32. 32.What is the sum of the first 12 terms of the AP 7, 10, 13, …? (a) 564 (b) 282 (c) 300 (d) 40
  33. 33.What is the sum of the first 6 terms of the AP 6, 8, 10, …? (a) 16 (b) 132 (c) 72 (d) 66
  34. 34.What is the sum of all the whole numbers from 1 to 92? (a) 8556 (b) 4232 (c) 4186 (d) 4278
  35. 35.What is the missing term in the AP 13, 17, ?, 25, 29? (a) 25 (b) 22 (c) 20 (d) 21
  36. 36.What is the sum of all the whole numbers from 1 to 68? (a) 2346 (b) 4692 (c) 2278 (d) 2312
  37. 37.Which term of the AP 17, 22, 27, 32, … is 187? (a) 36th (b) 35th (c) 34th (d) 37th
  38. 38.What is the 33rd term of the AP 12, 17, 22, 27, …? (a) 165 (b) 160 (c) 177 (d) 172
  39. 39.What is the missing term in the AP 3, 6, 9, ?, 15? (a) 13 (b) 11 (c) 15 (d) 12
  40. 40.What is the sum of the first 5 terms of the AP 1, 3, 5, …? (a) 25 (b) 9 (c) 30 (d) 50

Answer key

  1. 98
  2. 51
  3. 49
  4. 25
  5. 1128
  6. 153
  7. 22
  8. 191
  9. 152
  10. 354
  11. 111
  12. 19th
  13. 26th
  14. 135
  15. 17
  16. 1431
  17. 124
  18. 196
  19. 79
  20. 23
  21. 93
  22. 45
  23. 85
  24. 55
  25. 1326
  26. 88
  27. 16
  28. 144
  29. 351
  30. 54
  31. 216
  32. 282
  33. 66
  34. 4278
  35. 21
  36. 2346
  37. 35th
  38. 172
  39. 12
  40. 25

Free maths olympiad lessons, practice and worksheets at talentjr.in/maths-olympiad