Number Series

The series follows the pattern: 7*3+3=24, 24*3+3=75, 75*3+3=228, 228*3+3=687, 687*3+3=2064.

The differences are: 1.3, 2.6, 3.9, 6.9, 4.8, 7.8. The pattern of differences should be multiples of 1.3 (1.3, 2.6, 3.9, 5.2, 6.5, 7.8). Replacing 21.7 with 20.0 (14.8 + 5.2) makes the sequence consistent.

The pattern is subtracting consecutive multiples of 80, 80, 40, 40, 20, 20. Specifically: 324 - 160 = 164, 164 - 80 = 84, 84 - 40 = 44, 44 - 20 = 24, 24 - 10 = 14, 14 - 5 = 9. The term 46 breaks this sequence.

The pattern is: 5.5 * 3 = 16.5; 16.5 * 3 = 49.5; 49.5 * 3 = 148.5; 148.5 * 3 = 445.5. The term 450.5 is incorrect.

The pattern is: 8*2+15=31, 31*2+17=79, 79*2+11=169. The pattern of additions is 15, 17, 19, 21... If we use 15, 17, 19, 21, 23, 25: 8*2+15=31, 31*2+17=79, 79*2+19=177. The number 79 is the first point of deviation if the pattern is *2 + (odd numbers).

The differences are: 37-12=25, 73-37=36, 122-73=49, 186-122=64, 272-186=86, 367-272=95. The differences should be squares (5^2, 6^2, 7^2, 8^2, 9^2, 10^2). 86 and 95 are incorrect; 272 is the culprit.

Differences: 423-412=11, 444-423=21, 489-444=45, 577-489=88, 753-577=176, 1105-753=352. The pattern of differences is 11, 22, 44, 88, 176, 352. The second difference should be 22, so 423+22=445. 444 is the wrong number.

Series: 24, 120, 335, 720, 1320, 2184. 24 = 3^3 - 3, 120 = 5^3 - 5, 335 (should be 343-7=336), 720 = 9^3 - 9, 1320 = 11^3 - 11, 2184 = 13^3 - 13. The wrong number is 335.

The pattern is: 2*13=26, 26*11=286, 286*7=2002, 2002*5=10010, 10010*2=20020. The multipliers are primes in descending order: 13, 11, 7, 5, 3. Thus 10010*3 should be 30030.

Series: 250, 240, 230, 260, 200, 280, 190. Pattern: -10, -10, +30, -60, +80, -90. This is not a standard arithmetic series. If we look at alternating terms: 250, 230, 200, 190 (diff -20, -30, -10) and 240, 260, 280 (diff +20, +20). The term 200 breaks the pattern.

The pattern is division by 3, then multiplication by 6. 1080/3 = 360. 360*6 = 2160. 2160/9 = 240. 240*12 = 2880. 2880/15 = 192. 192*18 = 3456. The term 3450 is incorrect; it should be 3456.