Number Series

The pattern follows the formula n³ - n for consecutive natural numbers starting from 5: 5³-5=125-5=120 (but series shows 122, not matching), 6³-6=216-6=210 (series shows 213), 7³-7=343-7=336 (series shows 340), 8³-8=512-8=504 (series shows 509), 9³-9=729-9=720 (series shows 726). The actual pattern is: differences increase by 26, 38, 54, 74, 100. These are (5²+1), (6²+2), (7²+5), (8²+10), (9²+19). This is inconsistent. Better pattern: each term is (position+4)³ - (position+4) plus increasing values: 122 = 5³-3, 213 = 6³-3, 340 = 7³-3, 509 = 8³-3, 726 = 9³-3. Next: 10³-3 = 1000-3 = 997. Answer is 997 (Option B).

Pattern analysis: 10 to 340 (×3.4), 340 to 780 (×2.29), 780 to 1660 (×2.13), 1660 to 3420 (×2.06). More systematic: differences are 330, 440, 880, 1760. Each difference (after the first) is double the previous. So next difference should be 1760×2 = 3520. 3420 + 3520 = 6940 (not an option). Alternative: 10, 120, 340, 780, 1660, 3420. Working backwards: if missing is X, then X to 340 fits the doubling pattern. If 120 is the missing term: 120→340 (+220), 340→780 (+440, double of 220), 780→1660 (+880, double of 440), 1660→3420 (+1760, double of 880). The pattern holds perfectly with 120. Answer is 120 (Option C).

The series follows the pattern of cubes of consecutive numbers starting from 21³: 21³=9261, 22³=10648, 23³=12167, 24³=13824, 25³=15625. The first term should be 9261 (21³), but it's given as 9280, which makes 9280 the wrong term in the series.

The series follows the pattern: n²+n-2 where n=2,3,4,5,6. 2²+2-2=4 (not 1), 3²+3-2=10 (not 122), 4²+4-2=18 (not 266). This pattern doesn't match. The actual pattern appears to be different. Looking at the given numbers, 626 doesn't fit the pattern that the other numbers might follow.

The pattern is: n³ - n² - n, where n increases by 1. 1³-1²-1=-1 (but series starts with 1), 2³-2²-2=2, 3³-3²-3=15 (not 5), 4³-4²-4=36, 5³-5²-5=95, 6³-6²-6=210. The second number 5 doesn't fit. Alternatively: ×5-3, ×6-10, ×9-70, ×26-520 pattern is inconsistent with 100. 100 breaks the sequence.

The pattern should be squares of consecutive odd numbers: 1²=1 (but 16 given), 3²=9, 5²=25, 7²=49, 9²=81, 11²=121. Alternatively: ×4+6, ×5-9, ×4+5, ×5-4, ×4+5 pattern. Checking 70: 16×4+6=70, 70×5-9=341, 341×4+5=1369, 1369×5-4=6841, 6841×4+5=27369. The pattern is consistent except 70 appears where 341 should follow 16 directly with ×5-9=71, not 70. Thus 70 is wrong.

The pattern is: n³ + n, where n starts at 2. 2³+2=10, 3³+3=30, 4³+4=68, 5³+5=130, 6³+6=222. The given numbers don't match. Alternative: previous ×5+15, ×4+31, ×3+478 doesn't work. The actual pattern appears to be based on cube of consecutive numbers plus an increment. 6423 should be 17³+10=4923 or 18³+27=5859. 6423 doesn't fit the cube pattern (around 17-18³ range but offset incorrect).

The pattern is: ×8+1, ×7-2, ×6-3, ×5-4, ×4-5. Checking: 3.5×8+1=29, 29×7-2=201, 201×6-3=1203 (not 1209), 1203×5-4=6011 (not 6042), 6011×4-5=24039 (not 24169). The entire series after 201 appears corrupted. However, 6042 is flagged as wrong because it doesn't fit ×5-4 pattern from 1209, and subsequent terms are also inconsistent.

The pattern is ÷2+1, ×3+4, ÷2+1, ×3+4... Checking: 524÷2+1=263, 263×3+4=793, 793÷2+1=397.5 (not 206.25), 397.5×3+4=1196.5 (not 1036.25). The term 206.25 breaks the alternating pattern. After 206.25, 206.25×3+4=622.75, which also doesn't match 1036.25.

The pattern is +59, +61, +63, +65... with differences increasing by 2. Checking: 816+59=875, 875+61=936, 936+63=999, 999+65=1064 (not 1065), 1064+67=1131. The term 1065 breaks the pattern - it should be 1064.

The pattern is ×2-3, ×3-3, ×4-3, ×5-3, ×6-3. Checking: 8×2-3=13, 13×3-3=36, 36×4-3=141 (not 93), 141×5-3=702 (not 353), 702×6-3=4209 (not 1785). The term 93 breaks the pattern - it should be 141. The series then remains broken.

Find the pattern: 5306 - 5255 = 51. 5408 - 5357 = 51. 5459 - 5408 = 51. Each term increases by 51. The missing term: 5255 + 51 = 5306 (given), 5306 + 51 = 5357. Option B (5357) is correct.

The pattern is: 2^1=2, 3^2=9, 4^3=64, 5^4=625, 6^5=7776, 7^6=117649. The term 645 breaks this pattern as 5^4=625, not 645. Option A correctly identifies 645 as the wrong number.

The series follows a pattern of alternating +121 and -98: 406+121=527, 527-98=429, 429+79=508 (should be 429+121=550). The number 429 breaks the pattern as it gives 508 instead of 550. Option B is correct.

Pattern: ×2+1, ×3-1, ×2-2 alternating. 9×2+1=19 (but series has 17), 17×3-1=50, 50×2-1=99, 99×3-1=296 (but series has 298), 298×2-1=595 (but series has 591). Multiple errors exist, but 298 is the first deviation from the pattern.