Number Series

The series alternates between two patterns: 80, 70, 60 (subtract 10) and 10, 15, 20 (add 5). The next term follows the second pattern.

Pattern: 5*3+1=16, 16*3+3=51, 51*3+5=158. Next term: 158*3+7 = 474+7 = 481.

The numerators follow the pattern 2^n - 1 (3, 7, 15, 31, 63, 127). The denominators follow the recurrence relation d(n) = 3*d(n-1) + 1 (4, 13, 40, 121, 364, 1093). Thus, the missing term is 63/364.

The pattern is: 5*2+1=11, 11*2+2=24, 24*2+3=51, 51*2+4=106, 106*2+5=217. The term 216 is incorrect; it should be 217.

The pattern is: 1760 / 2 - 15 = 865; 865 / 2 - 12.5 = 420; 420 / 2 - 10 = 200 (not 210); 200 / 2 - 7.5 = 92.5. The number 210 is incorrect.

The pattern is +6, +3, +6, +3, +6, +3. 15+6=21, 21+3=24, 24+6=30, 30+3=33, 33+6=39, 39+3=42. The term 52 is incorrect; it should be 42.

The pattern is: 3.5 * 2 - 2 = 5; 5 * 2 - 2 = 8; 8 * 2 - 1 = 15 (should be 8 * 2 - 2 = 14); 14 * 2 - 2 = 26; 26 * 2 - 2 = 50; 50 * 2 - 2 = 98. The term 15 is incorrect.

The differences between consecutive terms are: 185-175=10, 205-185=20, 235-205=30, 275-235=40. The next difference should be 50. 275 + 50 = 325.

The series is two interleaved sequences: 0, 6, 20, 49 (first, third, fifth, seventh terms) and 6, 60, 210, 504 (second, fourth, sixth, eighth terms). The second sequence follows n(n+1)(n+2) for n=1, 3, 5, 7, but 49 is incorrect for the first sequence pattern.

The series follows a pattern of adding 3.5, then 7, then 3.5, then 7. 19 + 3.5 = 22.5; 22.5 + 7 = 29.5; 29.5 + 3.5 = 33; 33 + 7 = 40; 40 + 3.5 = 43.5 (not 42.5); 43.5 + 7 = 50.5. The wrong number is 42.5.

This is an arithmetic progression with first term a = 20 and common difference d = -5. The 15th term is a + (15-1)d = 20 + 14(-5) = 20 - 70 = -50.

Pattern: 888/2 + 10 = 454, 454/2 + 10 = 237, 237/2 + 10 = 128.5, 128.5/2 + 10 = 74.25 (not 76.25).

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