Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 43 · 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.Which term of the AP 16, 25, 34, 43, … is 115? (a) 14th (b) 11th (c) 13th (d) 12th
2. 2.What is the sum of the first 7 terms of the AP 8, 9, 10, …? (a) 14 (b) 78 (c) 77 (d) 154
3. 3.What is the sum of the first 8 terms of the AP 1, 3, 5, …? (a) 128 (b) 64 (c) 72 (d) 15
4. 4.What is the sum of the first 8 terms of the AP 8, 12, 16, …? (a) 352 (b) 36 (c) 192 (d) 176
5. 5.What is the 33rd term of the AP 11, 17, 23, 29, …? (a) 198 (b) 209 (c) 203 (d) 192
6. 6.Which term of the AP 4, 10, 16, 22, … is 202? (a) 34th (b) 33rd (c) 36th (d) 35th
7. 7.What is the sum of the first 11 terms of the AP 3, 7, 11, …? (a) 506 (b) 253 (c) 275 (d) 43
8. 8.What is the sum of the first 12 terms of the AP 4, 10, 16, …? (a) 444 (b) 70 (c) 888 (d) 480
9. 9.What is the 31st term of the AP 15, 22, 29, 36, …? (a) 225 (b) 210 (c) 217 (d) 232
10. 10.What is the sum of the first 6 terms of the AP 8, 14, 20, …? (a) 276 (b) 38 (c) 156 (d) 138
11. 11.What is the sum of the first 9 terms of the AP 2, 4, 6, …? (a) 18 (b) 180 (c) 90 (d) 99
12. 12.What is the 39th term of the AP 18, 21, 24, 27, …? (a) 132 (b) 114 (c) 135 (d) 117
13. 13.Which term of the AP 3, 5, 7, 9, … is 41? (a) 19th (b) 20th (c) 22nd (d) 21st
14. 14.What is the sum of the first 5 terms of the AP 1, 3, 5, …? (a) 50 (b) 30 (c) 25 (d) 9
15. 15.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 43 (b) 506 (c) 484 (d) 253
16. 16.What is the 23rd term of the AP 10, 12, 14, 16, …? (a) 56 (b) 46 (c) 44 (d) 54
17. 17.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 56 (b) 28 (c) 49 (d) 13
18. 18.What is the sum of all the whole numbers from 1 to 89? (a) 8010 (b) 3916 (c) 4006 (d) 4005
19. 19.What is the 18th term of the AP 18, 25, 32, 39, …? (a) 144 (b) 137 (c) 119 (d) 126
20. 20.Which term of the AP 6, 8, 10, 12, … is 62? (a) 28th (b) 29th (c) 31st (d) 30th
21. 21.What is the sum of all the whole numbers from 1 to 49? (a) 1176 (b) 1226 (c) 1225 (d) 2450
22. 22.What is the missing term in the AP 15, ?, 21, 24, 27? (a) 18 (b) 17 (c) 19 (d) 21
23. 23.What is the missing term in the AP 3, ?, 19, 27, 35? (a) 10 (b) 19 (c) 12 (d) 11
24. 24.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 25 (b) 91 (c) 182 (d) 169
25. 25.What is the 13th term of the AP 10, 16, 22, 28, …? (a) 72 (b) 88 (c) 82 (d) 78
26. 26.What is the missing term in the AP 16, ?, 22, 25, 28? (a) 18 (b) 19 (c) 20 (d) 22
27. 27.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 324 (b) 171 (c) 342 (d) 35
28. 28.Which term of the AP 5, 10, 15, 20, … is 145? (a) 31st (b) 28th (c) 30th (d) 29th
29. 29.What is the sum of all the whole numbers from 1 to 94? (a) 4371 (b) 4465 (c) 4418 (d) 8930
30. 30.What is the sum of all the whole numbers from 1 to 68? (a) 4692 (b) 2278 (c) 2312 (d) 2346
31. 31.What is the sum of all the whole numbers from 1 to 87? (a) 3741 (b) 3829 (c) 7656 (d) 3828
32. 32.What is the missing term in the AP 7, ?, 25, 34, 43? (a) 17 (b) 15 (c) 16 (d) 25
33. 33.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 378 (b) 729 (c) 53 (d) 756
34. 34.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 351 (b) 676 (c) 702 (d) 51
35. 35.What is the sum of all the whole numbers from 1 to 99? (a) 4951 (b) 4950 (c) 9900 (d) 4851
36. 36.What is the missing term in the AP 5, ?, 21, 29, 37? (a) 12 (b) 13 (c) 21 (d) 14
37. 37.What is the sum of the first 12 terms of the AP 8, 10, 12, …? (a) 240 (b) 228 (c) 30 (d) 456
38. 38.What is the 34th term of the AP 20, 23, 26, 29, …? (a) 119 (b) 102 (c) 122 (d) 99
39. 39.What is the sum of all the whole numbers from 1 to 92? (a) 4232 (b) 4278 (c) 8556 (d) 4186
40. 40.What is the 15th term of the AP 10, 19, 28, 37, …? (a) 135 (b) 136 (c) 145 (d) 126

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