Number Series

The pattern is: 12*3 + 2 = 38; 38*4 - 2 = 150; 150*5 + 2 = 752; 752*6 - 2 = 4510. The multiplier increases by 1 and the constant alternates between +2 and -2.

The differences between consecutive terms are: 2420-2325=95, 2325-2225=100, 2225-2115=110, 2115-1985=130. The differences of these differences are 5, 10, 20. The next difference should be 40. So, 130+40=170. 1985-170 = 1815.

7201, 7202 (x1+1), 3603 (x0.5+1), 1204 (x1/3+1), 306 (x1/4+1). 1204/4 + 1 = 301 + 1 = 302. The term 306 is incorrect.

The pattern is: 5*2+1=11, 11*2+1=23, 23*2+1=47, 47*2+1=95, 95*2+1=191. The term 192 is incorrect; it should be 191.

The pattern follows the rule: next term = (previous term * 2) - 1.4. For example, 18 * 2 - 1.4 = 34.6, and 34.6 * 2 - 1.4 = 67.8.

Pattern: 48*1+25=73, 73*2+27=173, 173*3+29=548? No. Let's check differences: 73-48=25 (5^2), 173-73=100 (10^2), 398-173=225 (15^2). Next difference should be 20^2 = 400. 398 + 400 = 798. Next difference 25^2 = 625. 798 + 625 = 1423. Matches.

Series: 3^1=3, 4^2=16, 5^3=125, 6^4=1296, 7^5=16807. Next is 8^6 = 262144.

The series is alternating operations: 6-1=5, 5*2.6=13 (no), 6-1=5, 5+8=13, 13*2.69=35 (no). Looking at pairs: (6,5), (13,35), (20,245), (27,?). The pattern is: 6*2+1=13, 13*2-6=20, 20*2-13=27. The second numbers are 5, 35, 245. 5*7=35, 35*7=245, 245*7=1715.

The series is an arithmetic progression with a common difference of 12. 13, 25, 37, 49, (49+12=61), 73, 85.

The sequence follows a pattern where each term is multiplied by 1/3 to get the next term. Starting with 9, 9 * 1/3 = 3, 3 * 1/3 = 1, 1 * 1/3 = 1/3, and 1/3 * 1/3 = 1/9.

The series is n^2 + n: 1^2+1=2, 2^2+2=6 (not 8), 3^2+3=12, 4^2+4=20, 5^2+5=30, 6^2+6=42, 7^2+7=56. The number 8 is incorrect.

The pattern is: 14 * 2 = 28; 28 * 4 = 112; 112 * 6 = 672; 672 * 8 = 5376. The term 5374 is wrong; it should be 5376.

The differences are: 18-6=12, 38-18=20, 66-38=28. The differences are increasing by 8 (12, 20, 28). The next difference should be 28+8=36. 66+36=102.

The pattern is x2 + 1: 23*2+1=47, 47*2+1=95, 95*2+1=191 (not 190), 191*2+1=383. The wrong number is 190.