Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 913 · 40 questions

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.

1. 1.What is the sum of the first 10 terms of the AP 5, 7, 9, …? (a) 23 (b) 280 (c) 140 (d) 150
2. 2.What is the 15th term of the AP 13, 21, 29, 37, …? (a) 133 (b) 112 (c) 120 (d) 125
3. 3.What is the 33rd term of the AP 6, 13, 20, 27, …? (a) 237 (b) 230 (c) 231 (d) 224
4. 4.What is the sum of the first 8 terms of the AP 1, 7, 13, …? (a) 200 (b) 176 (c) 43 (d) 352
5. 5.What is the 11th term of the AP 1, 5, 9, 13, …? (a) 41 (b) 45 (c) 40 (d) 44
6. 6.Which term of the AP 5, 12, 19, 26, … is 96? (a) 15th (b) 16th (c) 13th (d) 14th
7. 7.What is the sum of all the whole numbers from 1 to 66? (a) 2145 (b) 4422 (c) 2211 (d) 2178
8. 8.What is the sum of all the whole numbers from 1 to 69? (a) 2415 (b) 2416 (c) 4830 (d) 2346
9. 9.What is the 36th term of the AP 17, 22, 27, 32, …? (a) 192 (b) 180 (c) 197 (d) 175
10. 10.Which term of the AP 4, 12, 20, 28, … is 236? (a) 31st (b) 29th (c) 30th (d) 32nd
11. 11.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 17 (b) 90 (c) 81 (d) 45
12. 12.What is the 26th term of the AP 9, 15, 21, 27, …? (a) 150 (b) 159 (c) 156 (d) 165
13. 13.What is the sum of all the whole numbers from 1 to 83? (a) 3487 (b) 3403 (c) 6972 (d) 3486
14. 14.Which term of the AP 18, 21, 24, 27, … is 129? (a) 43rd (b) 39th (c) 38th (d) 37th
15. 15.What is the sum of the first 10 terms of the AP 8, 14, 20, …? (a) 62 (b) 380 (c) 350 (d) 700
16. 16.Which term of the AP 18, 21, 24, 27, … is 123? (a) 36th (b) 37th (c) 41st (d) 35th
17. 17.What is the missing term in the AP 12, ?, 24, 30, 36? (a) 19 (b) 18 (c) 17 (d) 24
18. 18.What is the sum of all the whole numbers from 1 to 37? (a) 666 (b) 1406 (c) 703 (d) 704
19. 19.What is the 21st term of the AP 13, 17, 21, 25, …? (a) 93 (b) 97 (c) 80 (d) 84
20. 20.What is the 31st term of the AP 9, 12, 15, 18, …? (a) 102 (b) 99 (c) 93 (d) 90
21. 21.What is the 16th term of the AP 16, 21, 26, 31, …? (a) 80 (b) 91 (c) 96 (d) 75
22. 22.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 27 (b) 105 (c) 210 (d) 196
23. 23.What is the 30th term of the AP 17, 20, 23, 26, …? (a) 87 (b) 107 (c) 90 (d) 104
24. 24.What is the 14th term of the AP 10, 12, 14, 16, …? (a) 26 (b) 28 (c) 38 (d) 36
25. 25.What is the 38th term of the AP 19, 22, 25, 28, …? (a) 111 (b) 114 (c) 133 (d) 130
26. 26.What is the 36th term of the AP 5, 10, 15, 20, …? (a) 180 (b) 175 (c) 181 (d) 185
27. 27.Which term of the AP 4, 6, 8, 10, … is 36? (a) 16th (b) 18th (c) 17th (d) 19th
28. 28.What is the sum of the first 6 terms of the AP 3, 4, 5, …? (a) 33 (b) 8 (c) 66 (d) 36
29. 29.What is the sum of the first 6 terms of the AP 5, 9, 13, …? (a) 90 (b) 102 (c) 180 (d) 25
30. 30.What is the missing term in the AP 16, 18, 20, ?, 24? (a) 23 (b) 24 (c) 22 (d) 21
31. 31.What is the missing term in the AP 2, 11, 20, ?, 38? (a) 29 (b) 30 (c) 38 (d) 28
32. 32.What is the sum of the first 12 terms of the AP 9, 10, 11, …? (a) 180 (b) 174 (c) 348 (d) 20
33. 33.What is the sum of the first 12 terms of the AP 8, 14, 20, …? (a) 984 (b) 492 (c) 74 (d) 528
34. 34.Which term of the AP 16, 23, 30, 37, … is 212? (a) 30th (b) 28th (c) 31st (d) 29th
35. 35.What is the sum of the first 12 terms of the AP 7, 11, 15, …? (a) 696 (b) 348 (c) 51 (d) 372
36. 36.What is the sum of the first 6 terms of the AP 6, 12, 18, …? (a) 36 (b) 126 (c) 144 (d) 252
37. 37.What is the missing term in the AP 14, 17, ?, 23, 26? (a) 23 (b) 20 (c) 19 (d) 21
38. 38.What is the sum of all the whole numbers from 1 to 77? (a) 6006 (b) 3003 (c) 3004 (d) 2926
39. 39.What is the missing term in the AP 16, 20, ?, 28, 32? (a) 28 (b) 24 (c) 23 (d) 25
40. 40.What is the 13th term of the AP 3, 6, 9, 12, …? (a) 40 (b) 36 (c) 42 (d) 39

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