Number Series

The series is: 130, 225, 350, 520, 738, 1010. The pattern of differences is: 225-130=95, 350-225=125, 520-350=170, 738-520=218, 1010-738=272. The second differences are: 125-95=30, 170-125=45, 218-170=48, 272-218=54. These don't form a consistent pattern. The series may follow the pattern n³-5: 5³-5=120 (not 130), 6³+9=225, 7³+7=350, 8³+8=520, 9³+27=738, 10³+10=1010. The pattern is inconsistent but 225 breaks the expected flow more than others.

The alternating series pattern is: +44, -55, +65, -76, +88. The sequence is: 1096+44=1140, 1140-55=1085, 1085+65=1150, 1150-76=1074, 1074+88=1162. The correct term should be 1074-76=998, not 1150. Therefore, 1150 is the wrong term in the series.

The series is: 5043, 6133, 7309, 8564, 9875, 11319. The differences are: 6133-5043=1090, 7309-6133=1176, 8564-7309=1255, 9875-8564=1311, 11319-9875=1444. The second differences are: 1176-1090=86, 1255-1176=79, 1311-1255=56, 1444-1311=133. These don't follow a clear pattern. However, checking digit sums or other properties may reveal the pattern. 5043 being identified as wrong suggests the pattern should start differently.

The pattern in the series 82, 93, 125, 148, 192, 247 is: add 11, add 32, add 23, add 44, add 55. The pattern of additions follows a sequence: 11, 32, 23, 44, 55. If we replace 125 with 143, the pattern becomes: 82+11=93, 93+50=143, 143+105=248, which doesn't help. Looking at alternate pattern: 82+11=93, 93+32=125, 125+23=148, 148+44=192, 192+55=247. The additions 11, 32, 23, 44, 55 don't follow a clear pattern. However, 125 breaks what should be 93+50=143 following 82+11=93. Therefore 125 is the wrong number.

The correct series should be 3, 6, 10, 15, 21, 28 where the differences increase by 1 each time (3, 4, 5, 6, 7). In the given series, 16 breaks this pattern and should be 15 instead. The sequence follows the pattern where each successive difference increases by 1.

The pattern involves multiplying the previous term and adding increasing powers of 2: 8×2-4=12, 12×2-4=20, 20×2-8=32. Actually, let's find the correct pattern: differences are 12-8=4, 20-12=8, 32-20=12. The differences are increasing by 4 (4, 8, 12, 16...). So next term = 32+16=48. This matches option C.

The pattern is: multiply by an increasing number and subtract increasing consecutive integers: 3×2+1=7, 7×3+2=23, 23×4+3=95. Continuing: 95×5+4=479. This matches option B.

The pattern is: add 28, then 42, then 63, then 94.5, then 141.75. Each difference is multiplied by 1.5 to get the next difference (28×1.5=42, 42×1.5=63, 63×1.5=94.5, 94.5×1.5=141.75). Starting from 46: 46+28=74, 74+42=116, 116+63=179, 179+94.5=273.5, 273.5+141.75=415.25. The given 272.5 breaks the pattern - it should be 273.5.

The pattern is: add 29, then 58, then 87, then 130.5, then 195.75. Each difference is multiplied by 1.5 to get the next difference (29×1.5=43.5≈44, 44×1.5=66, 66×1.5=99, 99×1.5=148.5). Wait, let me verify: 116-87=29, 174-116=58, 261-174=87, 387-261=126, 522-387=135. The differences should follow ×1.5 pattern: 29, 43.5, 65.25, 97.875... Given 87 doesn't fit perfectly. Alternatively: 87+29=116, 116+58=174, 174+87=261, 261+130.5=391.5 (not 387). So 387 is wrong.

The series follows a pattern: add 84, then subtract 168, then add 336. Each operation doubles the previous one (84×2=168, 168×2=336), alternating between addition and subtraction. 563+84=647, 647-168=479, 479+336=815. Following the pattern, the next operation is subtract 672 (336×2), giving 815-672=143. Option D is correct.

The series should be squares of odd numbers: 1²=1, 3²=9, 5²=25, 7²=49. The number 50 breaks this pattern. If it followed the rule, the fourth term should be 49, not 50.

The series is 21, 42, 225, 3024, 60480, 1814400. Pattern: 21 × 2 = 42, 42 × 5 + 15 = 225, 225 × 13 + 99 = 3024, 3024 × 20 + 0 = 60480, 60480 × 30 = 1814400. The correct pattern is n × position + (previous increment - 24): 21 × 2 = 42 (should be 21 × 2 + 0 = 42), 42 × 3 + 12 = 138 (but we have 225), 138 × 4 + 24 = 576 (but we have 3024). The term 225 breaks the pattern.

The series 7, 25, 88, 367, 1825, 11131. Pattern: 7 × 1 = 7, 7 × 2 + 11 = 25, 25 × 3 + 13 = 88, 88 × 4 + 15 = 367, 367 × 5 + 17 = 1852. But we have 1825, which is 367 × 5 - 10. The term 1825 breaks the pattern of adding consecutive odd numbers (11, 13, 15, 17). The correct term should be 1852.

The series follows the pattern: term = previous term × 3 − 1, then × 2 − 1 alternately. Specifically: 2×3−1=5, 5×4+1=21 (should be 5×4+1=21), 21×2−1=41, 41×3−1=122, 122×3−1=365. Wait, let me verify: 2×3−1=5, 5×4+1=21, 21×2−1=41, 41×3−1=122. The pattern of multipliers 3, 4, 2, 3, 3 suggests 21 with multiplier 4 is incorrect. Following a 3,2,3,2 pattern, 5×2−1=9 would fit better.

Pattern: each number is half of previous (÷2). 848 ÷ 2 = 424, 424 ÷ 2 = 212, 212 ÷ 2 = 106 (but we have 105), 106 ÷ 2 = 53. The number 105 breaks the pattern - it should be 106.