Directions (1-15): What will come in place of (?) in the following number series?
Q1. 5, 54, 397, 2798, ?, 137254
20605
19910
19605
18620
20520
Solution:

Q2. 625, 620, 613, 602, 589, 572, ?
541
537
531
521
553
Solution:
Series is –5, –7, –11, –13, –17, –19, –23(prime numbers)
∴ ? = 572– 19 = 553

Q3. 3, 6, 24, 144, ?, 11520
1158
1252
1125
1152
1212
Solution:
Series is ×2, ×4, ×6, ×8, ×10, ×12…..
∴ ? = 144 × 8 = 1152

Q4. 375000, 15000, 750, 50, 5, ?
1
2
4
5
3
Solution:
Series is ÷ 25, ÷ 20, ÷ 15, ÷ 10, ÷ 5
∴ ? = 5 ÷ 5 = 1

Q5. 1, 11, 81, 411, 1241, ?
1236
1251
1273
1237
1233
Solution:
Series is ×9+2, ×7+4, ×5+6, ×3+8, ×1+10
∴ ? = 1241 ×1+ 10 = 1251

Q6. 113, 130, 164, 215, ?, 368
293
273
283
327
372
Solution:
+17, +34, +51, +68, +85….

Q7. 112, 259, 392, 511, 616, ?
701
707
711
715
720
Solution:

Q8. 4, 6, 12, ?,90, 315, 1260
42
36
24
30
46
Solution:
×1.5, ×2, ×2.5, ×3 …

Q9. 6, 7, 16, 51, 208, ?, 6276
1045
941
836
1254
1154
Solution:
×1+1, ×2+2, ×3+3, ×4+4,…

Q10. 1130, 1164, 1232, 1334, 1470, ?
1674
1640
1606
1572
1623
Solution:
The pattern is +17×2, +17×4, +17×6, +17×8, +17×10…
∴ ? = 1470 + 17 × 10 = 1640

Q11. 353, 54, 380, 81, 444, 145, 569, ?, 785
209
361
270
226
488
Solution:

Q12. 2, 6, 21, 88, 445, ?
3122
2230
2766
2676
3568
Solution:
Pattern is ×2+2, ×3+3, ×4+4, ×5+5, ×6+6
∴ ? = 445 × 6+ 6 = 2676

Q13. 6, 15, 35, 77, 143, ?
195
247
221
225
241
Solution:
Pattern is (2×3), (3×5), (5×7), …….. Multiplication of two consecutive prime numbers
∴ ? = 13 × 17 = 221

Q14. 12, 6, 9, 22.5, 78.75, ?
345.375
354.375
374.535
375.435
343.755
Solution:
Pattern is ×0.5, ×1.5, ×2.5, ×3.5, ×4.5
∴ ? = 78.75 × 4.5 = 354.375

Q15. 51, 64, 116, 233, 441, 766, ?
1334
1234
1254
1285
1433
Solution:
Series is +13 × 1², + 13×2², +13×3², +13×4², +13×5², ….
∴ ? = 766 + 13 × 6² = 1234