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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 716 · 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 missing term in the AP 14, 16, ?, 20, 22? (a) 19 (b) 17 (c) 20 (d) 18
  2. 2.What is the missing term in the AP 4, ?, 20, 28, 36? (a) 11 (b) 13 (c) 20 (d) 12
  3. 3.What is the missing term in the AP 7, 15, 23, ?, 39? (a) 32 (b) 30 (c) 31 (d) 39
  4. 4.What is the sum of the first 10 terms of the AP 7, 8, 9, …? (a) 120 (b) 115 (c) 230 (d) 16
  5. 5.What is the 20th term of the AP 5, 13, 21, 29, …? (a) 160 (b) 157 (c) 165 (d) 152
  6. 6.What is the missing term in the AP 13, ?, 17, 19, 21? (a) 14 (b) 15 (c) 16 (d) 17
  7. 7.What is the sum of the first 8 terms of the AP 1, 7, 13, …? (a) 43 (b) 352 (c) 200 (d) 176
  8. 8.What is the sum of the first 10 terms of the AP 1, 2, 3, …? (a) 10 (b) 55 (c) 60 (d) 110
  9. 9.What is the 29th term of the AP 6, 12, 18, 24, …? (a) 175 (b) 180 (c) 168 (d) 174
  10. 10.Which term of the AP 1, 8, 15, 22, … is 127? (a) 18th (b) 20th (c) 21st (d) 19th
  11. 11.What is the missing term in the AP 15, 21, 27, ?, 39? (a) 32 (b) 34 (c) 33 (d) 39
  12. 12.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 9 (b) 30 (c) 15 (d) 25
  13. 13.What is the sum of the first 5 terms of the AP 3, 9, 15, …? (a) 75 (b) 150 (c) 27 (d) 90
  14. 14.What is the missing term in the AP 19, 23, 27, ?, 35? (a) 31 (b) 30 (c) 32 (d) 35
  15. 15.What is the sum of the first 12 terms of the AP 7, 10, 13, …? (a) 40 (b) 564 (c) 300 (d) 282
  16. 16.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 37 (b) 190 (c) 380 (d) 361
  17. 17.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 289 (b) 153 (c) 306 (d) 33
  18. 18.Which term of the AP 5, 8, 11, 14, … is 26? (a) 10th (b) 7th (c) 8th (d) 9th
  19. 19.What is the 21st term of the AP 12, 18, 24, 30, …? (a) 120 (b) 138 (c) 126 (d) 132
  20. 20.Which term of the AP 20, 23, 26, 29, … is 119? (a) 33rd (b) 34th (c) 36th (d) 35th
  21. 21.What is the missing term in the AP 5, ?, 15, 20, 25? (a) 15 (b) 9 (c) 10 (d) 11
  22. 22.What is the sum of all the whole numbers from 1 to 53? (a) 1378 (b) 1431 (c) 1432 (d) 2862
  23. 23.What is the sum of the first 12 terms of the AP 1, 7, 13, …? (a) 444 (b) 408 (c) 816 (d) 67
  24. 24.Which term of the AP 11, 14, 17, 20, … is 128? (a) 39th (b) 40th (c) 42nd (d) 41st
  25. 25.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 91 (b) 25 (c) 182 (d) 169
  26. 26.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 171 (b) 342 (c) 35 (d) 324
  27. 27.What is the 23rd term of the AP 14, 21, 28, 35, …? (a) 175 (b) 168 (c) 161 (d) 154
  28. 28.What is the 14th term of the AP 2, 5, 8, 11, …? (a) 41 (b) 44 (c) 39 (d) 42
  29. 29.What is the 15th term of the AP 11, 18, 25, 32, …? (a) 98 (b) 109 (c) 105 (d) 116
  30. 30.What is the 24th term of the AP 4, 6, 8, 10, …? (a) 48 (b) 46 (c) 52 (d) 50
  31. 31.What is the 29th term of the AP 12, 18, 24, 30, …? (a) 174 (b) 186 (c) 168 (d) 180
  32. 32.What is the sum of all the whole numbers from 1 to 66? (a) 2211 (b) 2178 (c) 4422 (d) 2145
  33. 33.What is the sum of the first 8 terms of the AP 7, 12, 17, …? (a) 392 (b) 196 (c) 42 (d) 216
  34. 34.What is the sum of all the whole numbers from 1 to 38? (a) 741 (b) 1482 (c) 722 (d) 703
  35. 35.What is the 36th term of the AP 16, 19, 22, 25, …? (a) 124 (b) 105 (c) 121 (d) 108
  36. 36.What is the 39th term of the AP 3, 11, 19, 27, …? (a) 312 (b) 307 (c) 315 (d) 304
  37. 37.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 210 (b) 420 (c) 400 (d) 39
  38. 38.What is the sum of the first 9 terms of the AP 3, 9, 15, …? (a) 270 (b) 51 (c) 243 (d) 486
  39. 39.What is the missing term in the AP 12, 19, ?, 33, 40? (a) 25 (b) 26 (c) 27 (d) 33
  40. 40.What is the sum of the first 7 terms of the AP 8, 10, 12, …? (a) 196 (b) 20 (c) 98 (d) 105

Answer key

  1. 18
  2. 12
  3. 31
  4. 115
  5. 157
  6. 15
  7. 176
  8. 55
  9. 174
  10. 19th
  11. 33
  12. 25
  13. 75
  14. 31
  15. 282
  16. 361
  17. 289
  18. 8th
  19. 132
  20. 34th
  21. 10
  22. 1431
  23. 408
  24. 40th
  25. 169
  26. 324
  27. 168
  28. 41
  29. 109
  30. 50
  31. 180
  32. 2211
  33. 196
  34. 741
  35. 121
  36. 307
  37. 400
  38. 243
  39. 26
  40. 98

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