Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 155 · 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 1, 6, 11, …? (a) 46 (b) 260 (c) 470 (d) 235
2. 2.Which term of the AP 13, 19, 25, 31, … is 241? (a) 41st (b) 39th (c) 38th (d) 40th
3. 3.What is the 34th term of the AP 15, 19, 23, 27, …? (a) 132 (b) 136 (c) 147 (d) 151
4. 4.What is the 34th term of the AP 10, 14, 18, 22, …? (a) 142 (b) 146 (c) 136 (d) 132
5. 5.What is the sum of the first 9 terms of the AP 4, 9, 14, …? (a) 216 (b) 221 (c) 44 (d) 432
6. 6.Which term of the AP 1, 10, 19, 28, … is 199? (a) 23rd (b) 25th (c) 24th (d) 22nd
7. 7.What is the sum of all the whole numbers from 1 to 90? (a) 4005 (b) 4050 (c) 4095 (d) 8190
8. 8.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 729 (b) 756 (c) 378 (d) 53
9. 9.What is the sum of all the whole numbers from 1 to 35? (a) 1260 (b) 631 (c) 630 (d) 595
10. 10.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 156 (b) 23 (c) 144 (d) 78
11. 11.What is the sum of the first 10 terms of the AP 8, 14, 20, …? (a) 350 (b) 380 (c) 700 (d) 62
12. 12.What is the 21st term of the AP 17, 25, 33, 41, …? (a) 177 (b) 160 (c) 185 (d) 168
13. 13.Which term of the AP 3, 5, 7, 9, … is 29? (a) 13th (b) 15th (c) 16th (d) 14th
14. 14.What is the 11th term of the AP 5, 9, 13, 17, …? (a) 44 (b) 45 (c) 40 (d) 49
15. 15.Which term of the AP 17, 19, 21, 23, … is 95? (a) 42nd (b) 40th (c) 41st (d) 39th
16. 16.What is the sum of the first 10 terms of the AP 8, 10, 12, …? (a) 26 (b) 170 (c) 180 (d) 340
17. 17.What is the 24th term of the AP 10, 14, 18, 22, …? (a) 102 (b) 106 (c) 92 (d) 96
18. 18.What is the sum of the first 6 terms of the AP 3, 9, 15, …? (a) 216 (b) 108 (c) 33 (d) 126
19. 19.What is the 40th term of the AP 13, 19, 25, 31, …? (a) 247 (b) 234 (c) 253 (d) 240
20. 20.What is the sum of the first 9 terms of the AP 6, 8, 10, …? (a) 22 (b) 135 (c) 252 (d) 126
21. 21.What is the 16th term of the AP 10, 12, 14, 16, …? (a) 30 (b) 42 (c) 40 (d) 32
22. 22.Which term of the AP 19, 26, 33, 40, … is 82? (a) 12th (b) 11th (c) 10th (d) 9th
23. 23.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 56 (b) 49 (c) 13 (d) 28
24. 24.What is the missing term in the AP 13, 15, ?, 19, 21? (a) 18 (b) 16 (c) 19 (d) 17
25. 25.What is the 11th term of the AP 6, 8, 10, 12, …? (a) 26 (b) 28 (c) 22 (d) 20
26. 26.What is the 24th term of the AP 1, 7, 13, 19, …? (a) 138 (b) 144 (c) 145 (d) 139
27. 27.Which term of the AP 10, 17, 24, 31, … is 185? (a) 28th (b) 25th (c) 27th (d) 26th
28. 28.What is the sum of the first 8 terms of the AP 8, 10, 12, …? (a) 120 (b) 22 (c) 240 (d) 128
29. 29.What is the sum of the first 6 terms of the AP 5, 11, 17, …? (a) 138 (b) 120 (c) 240 (d) 35
30. 30.What is the sum of all the whole numbers from 1 to 70? (a) 2415 (b) 2485 (c) 4970 (d) 2450
31. 31.What is the sum of all the whole numbers from 1 to 76? (a) 5852 (b) 2926 (c) 2888 (d) 2850
32. 32.What is the sum of the first 10 terms of the AP 1, 5, 9, …? (a) 210 (b) 37 (c) 380 (d) 190
33. 33.What is the 37th term of the AP 14, 17, 20, 23, …? (a) 108 (b) 111 (c) 122 (d) 125
34. 34.What is the missing term in the AP 3, ?, 9, 12, 15? (a) 6 (b) 5 (c) 9 (d) 7
35. 35.What is the missing term in the AP 18, 23, 28, ?, 38? (a) 33 (b) 34 (c) 32 (d) 38
36. 36.Which term of the AP 8, 14, 20, 26, … is 68? (a) 10th (b) 11th (c) 12th (d) 13th
37. 37.What is the sum of all the whole numbers from 1 to 45? (a) 1036 (b) 2070 (c) 1035 (d) 990
38. 38.What is the 14th term of the AP 10, 19, 28, 37, …? (a) 136 (b) 117 (c) 126 (d) 127
39. 39.What is the sum of all the whole numbers from 1 to 94? (a) 4418 (b) 8930 (c) 4465 (d) 4371
40. 40.What is the 38th term of the AP 12, 16, 20, 24, …? (a) 148 (b) 164 (c) 152 (d) 160

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