Number Series

The sequence follows the pattern: term(n) = term(n-1) * n + (n-1). For example: 8*1-1=7, 7*2+4=18, 18*4+13=85. This is a complex recursive pattern, and n=8 correctly yields the target value.

Series: 10, 14, 25, 55, 140. Differences: 4, 11, 30, 85. Second differences: 7, 19, 55. Pattern: 4*2+3=11, 11*2+8=30, 30*2+25=85. The next difference is 85*2 + 78 = 248. 140 + 248 = 388.

The differences are: 131-119=12, 155-131=24, 191-155=36, 239-191=48. The differences are multiples of 12. The next difference should be 60. 239 + 60 = 299.

Differences: 697-553=144 (12^2), 553-453=100 (10^2), 453-389=64 (8^2), 389-353=36 (6^2). Next difference should be 4^2 = 16. 353 - 16 = 337.

The pattern is division by a decreasing sequence: 336/1.5 = 224, 224/1.33 = 168 (or more simply, the differences are 112, 56, 28, 14, 7). The differences are halved each time. 126 - 7 = 119.

The series is 6, 10, 18, 34. Differences: 4, 8, 16. The next difference should be 32. 34 + 32 = 66.

The series is 7, 12, 25, 22, 43, ?. Alternating series: 7, 25, 43 (add 18) and 12, 22, ? (add 10). 22 + 10 = 32.

The series follows an alternating pattern: +6, -4, +6, -4, +6. Following 27, the next step is 27 - 4 = 23.

The series consists of squares: 17^2=289, 16^2=256, 15^2=225, 14^2=196. The next is 13^2 = 169.

The pattern is: 20-1=19, 19-2=17, 17-3=14, 14-4=10, 10-5=5. The missing number is 14.

The differences between consecutive terms are: 7-2=5, 17-7=10, 32-17=15, 52-32=20. The differences follow an arithmetic progression increasing by 5. The next difference should be 25, so 52+25=77.

The sequence is 2*6=12, 12*5=60, 60*4=240, 240*3=720, 720*2=1440, 1440*1=1440.

The terms in the series are obtained by multiplying the preceding term by consecutive integers starting from 2. Specifically, 27 * 2 = 54, 54 * 3 = 162, 162 * 4 = 648, 648 * 5 = 3240, and 3240 * 6 = 19440. Thus, the missing number is 3240.