← Sequences and AP lesson New set →

Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 236 · 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) 231 (b) 228 (c) 225 (d) 222
  2. 2.What is the missing term in the AP 17, ?, 23, 26, 29? (a) 19 (b) 21 (c) 20 (d) 23
  3. 3.What is the missing term in the AP 16, 18, 20, ?, 24? (a) 24 (b) 23 (c) 22 (d) 21
  4. 4.Which term of the AP 4, 8, 12, 16, … is 84? (a) 22nd (b) 23rd (c) 20th (d) 21st
  5. 5.What is the sum of all the whole numbers from 1 to 33? (a) 1122 (b) 562 (c) 528 (d) 561
  6. 6.What is the 23rd term of the AP 20, 24, 28, 32, …? (a) 88 (b) 92 (c) 112 (d) 108
  7. 7.What is the sum of all the whole numbers from 1 to 31? (a) 496 (b) 497 (c) 992 (d) 465
  8. 8.What is the 12th term of the AP 14, 22, 30, 38, …? (a) 110 (b) 88 (c) 96 (d) 102
  9. 9.What is the sum of the first 5 terms of the AP 6, 12, 18, …? (a) 30 (b) 180 (c) 105 (d) 90
  10. 10.What is the sum of all the whole numbers from 1 to 39? (a) 741 (b) 781 (c) 1560 (d) 780
  11. 11.What is the missing term in the AP 2, 10, 18, ?, 34? (a) 25 (b) 34 (c) 27 (d) 26
  12. 12.What is the sum of the first 7 terms of the AP 3, 4, 5, …? (a) 43 (b) 84 (c) 9 (d) 42
  13. 13.What is the sum of the first 12 terms of the AP 6, 12, 18, …? (a) 504 (b) 72 (c) 468 (d) 936
  14. 14.Which term of the AP 11, 17, 23, 29, … is 221? (a) 36th (b) 35th (c) 38th (d) 37th
  15. 15.What is the missing term in the AP 1, ?, 7, 10, 13? (a) 4 (b) 7 (c) 3 (d) 5
  16. 16.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 42 (c) 11 (d) 36
  17. 17.What is the 19th term of the AP 11, 19, 27, 35, …? (a) 144 (b) 152 (c) 155 (d) 163
  18. 18.What is the 35th term of the AP 10, 14, 18, 22, …? (a) 150 (b) 136 (c) 146 (d) 140
  19. 19.What is the sum of all the whole numbers from 1 to 56? (a) 1540 (b) 1596 (c) 1568 (d) 3192
  20. 20.What is the sum of the first 8 terms of the AP 7, 9, 11, …? (a) 112 (b) 120 (c) 21 (d) 224
  21. 21.What is the missing term in the AP 2, 11, ?, 29, 38? (a) 29 (b) 19 (c) 21 (d) 20
  22. 22.What is the 16th term of the AP 3, 6, 9, 12, …? (a) 48 (b) 45 (c) 51 (d) 49
  23. 23.What is the 33rd term of the AP 12, 17, 22, 27, …? (a) 172 (b) 160 (c) 165 (d) 177
  24. 24.Which term of the AP 20, 23, 26, 29, … is 68? (a) 19th (b) 18th (c) 17th (d) 16th
  25. 25.What is the 18th term of the AP 20, 23, 26, 29, …? (a) 74 (b) 54 (c) 51 (d) 71
  26. 26.What is the sum of the first 12 terms of the AP 4, 5, 6, …? (a) 120 (b) 15 (c) 228 (d) 114
  27. 27.What is the 32nd term of the AP 3, 6, 9, 12, …? (a) 96 (b) 97 (c) 93 (d) 99
  28. 28.What is the missing term in the AP 12, 14, 16, ?, 20? (a) 18 (b) 19 (c) 20 (d) 17
  29. 29.What is the 21st term of the AP 14, 17, 20, 23, …? (a) 60 (b) 74 (c) 63 (d) 77
  30. 30.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 210 (b) 400 (c) 420 (d) 39
  31. 31.Which term of the AP 1, 10, 19, 28, … is 118? (a) 14th (b) 15th (c) 16th (d) 13th
  32. 32.What is the sum of the first 5 terms of the AP 4, 10, 16, …? (a) 95 (b) 80 (c) 28 (d) 160
  33. 33.What is the 15th term of the AP 3, 12, 21, 30, …? (a) 129 (b) 126 (c) 138 (d) 135
  34. 34.What is the 31st term of the AP 18, 22, 26, 30, …? (a) 124 (b) 138 (c) 142 (d) 120
  35. 35.What is the 40th term of the AP 8, 15, 22, 29, …? (a) 281 (b) 288 (c) 273 (d) 280
  36. 36.What is the sum of the first 5 terms of the AP 8, 9, 10, …? (a) 100 (b) 50 (c) 51 (d) 12
  37. 37.What is the missing term in the AP 11, ?, 19, 23, 27? (a) 16 (b) 15 (c) 14 (d) 19
  38. 38.What is the sum of the first 7 terms of the AP 7, 13, 19, …? (a) 43 (b) 196 (c) 350 (d) 175
  39. 39.Which term of the AP 1, 8, 15, 22, … is 148? (a) 22nd (b) 24th (c) 21st (d) 23rd
  40. 40.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 66 (b) 132 (c) 121 (d) 21

Answer key

  1. 225
  2. 20
  3. 22
  4. 21st
  5. 561
  6. 108
  7. 496
  8. 102
  9. 90
  10. 780
  11. 26
  12. 42
  13. 468
  14. 36th
  15. 4
  16. 36
  17. 155
  18. 146
  19. 1596
  20. 112
  21. 20
  22. 48
  23. 172
  24. 17th
  25. 71
  26. 114
  27. 96
  28. 18
  29. 74
  30. 400
  31. 14th
  32. 80
  33. 129
  34. 138
  35. 281
  36. 50
  37. 15
  38. 175
  39. 22nd
  40. 121

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