Number Series

Sequence: 5, 7, 11, 19. Differences: 2, 4, 8. This is a geometric progression of differences (2^1, 2^2, 2^3). Next differences: 16, 32, 64, 128. Terms: 19+16=35 (5th), 35+32=67 (6th), 67+64=131 (7th), 131+128=259 (8th).

a + 9d = 6, a + 17d = 70. Subtracting: 8d = 64, so d = 8. a + 9(8) = 6 => a + 72 = 6 => a = -66.

The sequence is 20 (+10) = 30, 30 (+18) = 48, 48 (+8) = 56, 56 (+16) = 72, 72 (+18) = 90. The pattern of differences is 10, 18, 8, 16, 18. If the series were 20, 32, 44, 56, 68, 80 or similar, it would be consistent. However, looking at the differences: 10, 18, 8, 16, 18, the number 48 is the outlier that breaks the progression.

The differences are 9, 16, 25, 36. These are squares of 3, 4, 5, 6. The next difference should be 7^2 = 49. 91 + 49 = 140.

Differences: 356-345=11, 368-356=12, 381-368=13, 395-381=14. The next difference should be 15. 395 + 15 = 410.

The pattern is multiplying by 1.5, 2.5, 3.5, 4.5, 5.5. 144 * 1.5 = 216 (not 215). 216 * 2.5 = 540. The wrong number is 215.

The series increases by a constant difference of 34 (62-28=34, 96-62=34, etc.). Adding 34 to 164 gives 198.

The pattern is: 1*2+7=9, 9*3+6=33, 33*4+5=137. The term 105 is incorrect; it should be 137. Following the pattern 137*5+4=689, the series is inconsistent.