Directions (Q.1-26): Find the missing term in the given series:
1. 32, 75, 144, 244 ......, 567.
A) 380 B) 384 C) 390 D) 395
Sol: 1 + 22 + 33 = 32
2 + 32 + 43 = 75
3 + 42 + 53 = 144
4 + 52 + 63 = 244
5 + 62 + 73 = 384
6 + 72 + 83 = 567
Ans: B
2. 380, 391, 413, 446, ?, 545
A) 510 B) 500 C) 450 D) 490
Sol: 380 + 11 = 391
391 + 22 = 413
413 + 33 = 446
446 + 44 = 490
490 + 55 = 545
Ans: D
3. 10, 70, 420, 2100, 8400, ......, 50400
A) 25200 B) 25000 C) 19800 D) 24000
Sol: 10 × 7 = 70
70 × 6 = 420
420 × 5 = 2100
2100 × 4 = 8400
8400 × 3 = 25200
25200 × 2 = 50400
Ans: A
4. 400, 300, 219, 155, 106, ....., 45
A) 80 B) 65 C) 70 D) 90
Sol: 400 − 102 = 300
300 − 92 = 219
219 − 82 = 155
155 − 72 = 106
106 − 62 = 70
70 − 52 = 45
Ans: C
5. 40, 46, 56, 70, 88, ......., 136
A) 100 B) 110 C) 120 D) 125
Sol: 40 + 6 = 46
46 + 10 = 56
56 + 14 = 70
70 + 18 = 88
88 + 22 = 110
110 + 26 = 136
Ans: B
6. 10, 22, 46, 94, ......., 382, 766
A) 180 B) 188 C) 190 D) 194
Sol: 10 × 2 + 2 = 22
22 × 2 + 2 = 46
46 × 2 + 2 = 94
94 × 2 + 2 = 190
190 × 2 + 2 = 382
382 × 2 + 2 = 766
Ans: C
7. 50, ......, 386, 770, 1538, 3074
A) 96 B) 94 C) 52 D) 98
Sol: 50 × 2 − 2 = 98
98 × 2 − 2 = 194
194 × 2 − 2 = 386
386 × 2 − 2 = 770
770 × 2 − 2 = 1538
1538 × 2 − 2 = 3074
Ans: D
8. 16, 50, ......, 458, 1376, 4130
A) 160 B) 140 C) 152 D) 175
Sol: 16 × 3 + 2 = 50
50 × 3 + 2 = 152
152 × 3 + 2 = 458
458 × 3 + 2 = 1376
1376 × 3 + 2 = 4130
Ans: C
9. 40, 77, 151, ......, 595 , 1187 , 2371
A) 265 B) 271 C) 280 D) 299
Sol: 40 × 2 − 3 = 77
77 × 2 − 3 = 151
151 × 2 − 3 = 299
299 × 2 − 3 = 595
595 × 2 − 3 = 1187
1187 × 2 − 3 = 2371
Ans: D
10. 16, 20, 36, 56, 92, 148, 240, .......
A) 404 B) 414 C) 340 D) 388
Sol: 16 + 20 = 36
20 + 36 = 56
36 + 56 = 92
56 + 92 = 148
92 + 148 = 240
148 + 240 = 388
Ans: D
11. 10, 30, ......, 150, 310, 630, 1270
A) 40 B) 50 C) 60 D) 70
Sol: 10 × 2 + 10 = 30
30 × 2 + 10 = 70
70 × 2 + 10 = 150
150 × 2 + 10 = 310
310 × 2 + 10 = 630
630 × 2 + 10 = 1270
Ans: D
12. 70, 151, 215, 264, 300, 325, .......
A) 312 B) 321 C) 314 D) 341
Sol: 70 + 92 = 151
151 + 82 = 215
215 + 72 = 264
264 + 62 = 300
300 + 52 = 325
325 + 42 = 341
Ans: D
13. 30, 63, 130, 525, ......, 15793
A) 2424 B) 2462 C) 2514 D) 2631
Sol: 30 × 2 + 3 = 63
63 × 3 + 4 = 130
130 × 4 + 5 = 525
525 × 5 + 6 = 2631
2631 × 6 + 7 = 15793
Ans: D
14. 12, 53, ......, 873, 3497, 13993
A) 187 B) 197 C) 207 D) 217
Sol: 12 × 4 + 5 = 53
53 × 4 + 5 = 217
217 × 4 + 5 = 873
873 × 4 + 5 = 3497
3497 × 4 + 5 = 13993
Ans: D
15. 40, 89, 187, 383, 775, 1559, .......
A) 3127 B) 3230 C) 3060 D) 3340
Sol: 40 × 2 + 9 = 89
89 × 2 + 9 = 187
187 × 2 + 9 = 383
383 × 2 + 9 = 775
775 × 2 + 9 = 1559
1559 × 2 + 9 = 3127
Ans: A
16. 9, 35, 138, 549, ......, 8763
A) 2092 B) 2192 C) 1992 D) 2292
Sol: 9 × 4 − 1 = 35
35 × 4 − 2 = 138
138 × 4 − 3 = 549
549 × 4 − 4 = 2192
2192 × 4 − 5 = 8763
Ans: B
17. 6, 14, ......, 62, 126, 254, 510
A) 20 B) 42 C) 30 D) 25
Sol: 6 × 2 + 2 = 14
14 × 2 + 2 = 30
30 × 2 + 2 = 62
62 × 2 + 2 = 126
126 × 2 + 2 = 254
254 × 2 + 2 = 510
Ans: C
18. 9, 8, 14, 39, ......, 755, 4524
A) 152 B) 151 C) 171 D) 172
Sol: 9 × 1 − 1 = 8
8 × 2 − 2 = 14
14 × 3 − 3 = 39
39 × 4 − 4 = 152
152 × 5 − 5 = 755
755 × 6 − 6 = 4524
Ans: A
19. 15, 19, 42, 130, 524, .......
A) 2523 B) 2620 C) 2124 D) 2624
Sol: 15 × 1 + 4 = 19
19 × 2 + 4 = 42
42 × 3 + 4 = 130
130 × 4 + 4 = 524
524 × 5 + 4 = 2624
Ans: D
20. 10, 25, 70, 205, 610, ......, 5470
A) 1875 B) 1795 C) 1815 D) 1825
Sol: 10 × 3 − 5 = 25
25 × 3 − 5 = 70
70 × 3 − 5 = 205
205 × 3 − 5 = 610
610 × 3 − 5 = 1825
1825 × 3 − 5 = 5470
Ans: D
21. 10, 9, 16, 45, 176, 875, .......
A) 5644 B) 5624 C) 5244 D) 5544
Sol: 10 × 1 − 1 = 9
9 × 2 − 2 = 16
16 × 3 − 3 = 45
45 × 4 − 4 = 176
176 × 5 − 5 = 875
875 × 6 − 6 = 5244
Ans: C
22. 12, 24, ......, 288, 1440, 8640, 60480
A) 64 B) 68 C) 70 D) 72
Sol: 12 × 2 = 24
24 × 3 = 72
72 × 4 = 288
288 × 5 = 1440
1440 × 6 = 8640
8640 × 7 = 60480
Ans: D
23. 16, 24, 48, 120, 360, ......, 5040
A) 1060 B) 1260 C) 1360 D) 1560
Sol: 16 × 1.5 = 24
24 × 2 = 48
48 × 2.5 = 120
120 × 3 = 360
360 × 3.5 = 1260
1260 × 4 = 5040
Ans: B
24. 15, 17, 21, 29, 45, 77, .......
A) 141 B) 150 C) 161 D) 171
Sol: 15 + 2 = 17
17 + 4 = 21
21 + 8 = 29
29 + 16 = 45
45 + 32 = 77
77 + 64 = 141
Ans: A
25. 8, 26, 62, 134, ......, 566, 1142
A) 280 B) 278 C) 270 D) 288
Sol: 8 × 2 + 10 = 26
26 × 2 + 10 = 62
62 × 2 + 10 = 134
134 × 2 + 10 = 278
278 × 2 + 10 = 566
566 × 2 + 10 = 1142
Ans: B
26. 8, 32, 160, ......, 6720, 53760
A) 964 B) 960 C) 970 D) 972
Sol: 8 × 4 = 32
32 × 5 = 160
160 × 6 = 960
960 × 7 = 6720
6720 × 8 = 53760
Ans: B
Some more...
Directions (Qs. 1 - 21): Select the number from among the given options that can replace the question mark (?) in the following series.
1. 9, 27, 81, 243, 729, ?
A) 2817 B) 2187 C) 2278 D) 2619
Ans: B
2. 6, 24, 54, 96, ?, 216
A) 144 B) 128 C) 126 D) 150
Ans: D
3. 7200, 1440, 360, 120, 60, ?
A) 6 B) 120 C) 60 D) 30
Ans: C
4. 10, 29, 66, 127, 218, ?
A) 345 B) 346 C) 347 D) 348
Ans: A
5. 20, 35, 53, 74, 98, ?
A) 121 B) 120 C) 140 D) 125
Ans: D
6. 33, 65, 129, 257, 513, ?
A) 1025 B) 1024 C) 1026 D) 1030
Ans: A
7. 23, 120, 605, 3030, ?
A) 14055 B) 15055 C) 15155 D) 14155
Ans: C
8. 10, 73, 505, 3025, 15121, ?
A) 60148 B) 60841 C) 60481 D) 60418
Ans: C
9. 20, 46, 66, 112, 178, 290, ?
A) 448 B) 468 C) 478 D) 470
Ans: B
10. 81, 27, 54, 18, 36, 12, ?
A) 27 B) 24 C) 28 D) 48
Ans: B
11. 16, 35, 109, 441, 2211, ?
A) 13723 B) 13373 C) 13273 D) 13370
Ans: C
12. 15, 13, 23, 65, 255, ?
A) 1269 B) 1296 C) 1261 D) 1265
Ans: A
13. 6, 47, 328, 1967, 9834, ?
A) 39135 B) 39343 C) 39345 D) 39335
Ans: D
14. 69, 70, 74, 90, 154, ?
A) 410 B) 420 C) 400 D) 415
Ans: A
15. 59, 60, 62, 71, 135, ?
A) 840 B) 1035 C) 760 D) 670
Ans: C
16. 256, 192, 144, 108, ?
A) 81 B) 243 C) 75 D) 60
Ans: A
17. 81, 246, 741, 2226, 6681, ?
A) 20046 B) 20064 C) 20061 D) 20604
Ans: A
18. 6, 7, 15, 42, 106, ?
A) 216 B) 204 C) 201 D) 231
Ans: D
19. 15, 95, 159, 207, 239, ?
A) 250 B) 254 C) 255 D) 256
Ans: C
20. 3125, 625, 125, 25, 5, ?
A) 1 B) 5 C) 4 D)1/5
Ans: A
21. 1728, 2197, 2744, 3375, ?
A) 4906 B) 4096 C) 4609 D) 4690
Ans: B
Explanations
1. Series pattern:
Every next element
= 3 × Previous element
9 × 3 = 27, 27 × 3 = 81,
81 × 3 = 243, 243 × 3 = 729
So, 729 × 3 = 2187
Therefore, Missing term = 2187.
2. 6 × 12 = 6, 6 × 22 = 24, 6 × 32 = 54
6 × 42 = 96, 6 × 52 = 150,
6 × 62 = 216
So, the missing term should be 150.
3. 7200 ÷ 5 = 1440, 1440 ÷ 4 = 360,
360 ÷ 3 = 120, 120 ÷ 2 = 60,
60 ÷ 1 = 60
So, the missing term should be 60.
4. 23 + 2 = 10, 33 + 2 = 29,
43 + 2 = 66
53 + 2 = 127, 63 + 2 = 218
So, similarly 73 + 2 = 345
5. 20 + 15 = 35, 35 + 18 = 53,
53 + 21 = 74, 74 + 24 = 98,
98 + 27 = 125
So, missing term = 125
6. 33 × 2 − 1 = 65, 65 × 2 − 1 = 129
129 × 2 − 1 = 257
257 × 2 − 1 = 513
513 × 2 − 1 = 1025
7. 23 × 5 + 5 = 120, 120 × 5 + 5 = 605
605 × 5 + 5 = 3030
3030 × 5 + 5 = 15155
8. 10 × 8 − 7 = 73, 73 × 7 − 6 = 505
505 × 6 − 5 = 3025
3025 × 5 − 4 = 15121
15121 × 4 − 3 = 60481
9. In this series each term is the addition of the two previous terms.
20 + 46 = 66, 46 + 66 = 112,
66 + 112 = 178,
112 + 178 = 290
178 + 290 = 468
10. 81 ÷ 3 = 27, 27 × 2 = 54
54 ÷ 3 = 18, 18 × 2 = 36
36 ÷ 3 = 12, 12 × 2 = 24
11. 16 × 2 + 3 = 35, 35 × 3 + 4 = 109
109 × 4 + 5 = 441,
441 × 5 + 6 = 2211
2211 × 6 + 7 = 13273
12. 15 × 1 − 2 = 13, 13 × 2 − 3 = 23
23 × 3 − 4 = 65, 65 × 4 − 5 = 255
255 × 5 − 6 = 1269
13. 6 × 8 − 1 = 47, 47 × 7 − 1 = 328
328 × 6 − 1 = 1967
1967 × 5 − 1 = 9834
9834 × 4 − 1 = 39335
14. 69 + 40 = 69 + 1 = 70
70 + 41 = 70 + 4 = 74
74 + 42 = 74 + 16 = 90
90 + 43 = 90 + 64 = 154
154 + 44 = 154 + 256 = 410
15. 59 + 10 = 60, 60 + 21 = 62
62 + 32 = 71, 71 + 43 = 135
135 + 54 = 760
16. 
17. 81 × 3 + 3 = 246
246 × 3 + 3 = 741
741 × 3 + 3 = 2226
2226 × 3 + 3 = 6681
6681 × 3 + 3 = 20046
18. 6 + 13 = 7, 7 + 23 = 15,
15 + 33 = 42, 42 + 43 = 106,
106 + 53 = 231
19. 15 + 80 = 95, 95 + 64 = 159,
159 + 48 = 207, 207 + 32 = 239,
239 + 16 = 255
Above are 16 multiples.
20. 3125 ÷ 5 = 625, 625 ÷ 5 = 125
125 ÷ 5 = 25, 25 ÷ 5 = 5,
5 ÷ 5 = 1
21. 123 = 1728, 133 = 2197
143 = 2744,
153 = 3375, 163 = 4096
