Number Series

The series follows a pattern of subtracting decreasing multiples of 10: 3980 - 600 = 3380; 3380 - 510 = 2870; 2870 - 438 = 2432; 2432 - 382 = 2050; 2050 - 330 = 1720; 1720 - 320 = 1400. The pattern of differences is 600, 510, 438, 382, 330, 320. The sequence of differences of differences is 90, 72, 56, 52, 10. The term 1720 is incorrect because it breaks the progression of the differences.

The pattern of the series is that each term is multiplied by its position index and then the square of that index is added to it. Specifically, the formula is term(n) = term(n-1) * n + n^2. Applying this, the second term should be 4 * 1 + 1^2 = 5, making 6 the wrong number in the series.

The pattern is multiplication by 3, 2, 3, 2, 3, 2. 40 * 3 = 120, 120 * 2 = 240, 240 * 3 = 720, 720 * 2 = 1440 (not 1400), 1440 * 3 = 4320, 4320 * 2 = 8640. 1400 is the wrong number.

Pattern: 900-4=896, 896+16=912, 912-64=848, 848+256=1104. The number 1105 is wrong; it should be 1104.

Pattern: x * 0.5 + 2.4. 2 * 0.5 + 2.4 = 3.4. 3.4 * 0.5 + 2.4 = 4.1 (not 6.2). The series is inconsistent.

The pattern is x(n) = x(n-1) * 3 + 1. 1*3+1=4, 4*3+1=13, 13*3+1=40, 40*3+1=121.

The pattern is: 2*2-1=3, 3*3+2=11, 11*4-6=38, 38*5+11=201. The term 101 is incorrect; it should be 201.

The differences between consecutive terms are 5, 7, 9, 11. The next difference should be 13. 38 + 13 = 51. Then 51 + 15 = 66, which matches.

This is a geometric progression with a = 1/27 and r = 3. The n-th term is a * r^(n-1) = 729. (1/27) * 3^(n-1) = 729. 3^(n-1) = 729 * 27 = 3^6 * 3^3 = 3^9. n - 1 = 9, so n = 10.

The differences are: 1541-1524=17, 1576-1541=35, 1626-1576=50, 1694-1626=68, 1779-1694=85. The pattern of differences should be 17, 34, 51, 68, 85 (multiples of 17). 1576 is incorrect because 1541+34=1575.

Pattern: 169 (+15) = 184; 184 (-45) = 139; 139 (+75) = 214 (not 216); 214 (-105) = 109; 109 (+135) = 244. The pattern is +15, -45, +75, -105, +135. 216 is the wrong number.