Number Series

The series pattern is: differences are +3, +10, +14, +27, +35, +50. Looking closer: 19 to 22 (+3), 22 to 32 (+10), 32 to 46 (+14), 46 to 73 (+27), 73 to 108 (+35), 108 to 158 (+50). The pattern of differences appears irregular. 46 doesn't fit the expected sequence based on preceding terms.

The series follows the pattern: +86, +97, +110, +128, +181, +181. The differences should increase: 45 to 131 is +86, 131 to 228 is +97, 228 to 338 is +110, 338 to 466 is +128, 466 to 619 is +153, 619 to 800 is +181. The term 466 is incorrect as the pattern breaks there.

The series is factorials: 1x1=1, 1x2=2, 2x3=6, 6x4=24, 24x5=120, 120x6=720, 720x7=5040, 5040x8=40320. So 121 is incorrect (should be 120) and 5040 is correct.

The series 672, 666, 660, 654 decreases by 6 each time: 672−6=666, 666−6=660, 660−6=654. Continuing this pattern, 654−6=648. Option B (646) would require decreasing by 8, option C (650) would require an increase of 4, and option D (640) would require decreasing by 14, none of which follow the pattern.

The series is squares of odd numbers: 1²=1, 3²=9, 5²=25, 7²=49, 9²=81, 11²=121, 13²=169, 15²=225, 17²=289. First bracketed number 81 is correct (9²). Second bracketed number 215 is incorrect (should be 225, which is 15²).

The series follows a cube multiplication pattern: ×1+10, ×3+6, ×5+20, ×7-140, ×9-450. Starting with 8: 8×1+10=18, 18×3+6=60 (not 80), 60×5+20=320 (not 420). If 80 is wrong, the correct term after 18 should be 60. Continuing: 60×5+20=320, 320×7-140=2100 (not 2420). The pattern of multipliers 1,3,5,7,9 (odd numbers) suggests 80 should be 60.

The pattern is decreasing differences by 2 each time. 891-684=207, 684-479=205, 479-276=203, 276-75=201. Each successive difference decreases by 2.

Find the pattern: 15 = 2×8 - 1 = 15; 29 = 2×15 - 1 = 29; 57 = 2×29 - 1 = 57; 113 = 2×57 - 1 = 113. The rule is: next term = 2×(previous term) - 1. Next term = 2×113 - 1 = 225.

The differences between consecutive terms are: 100-10=90, 200-100=100, 310-200=110. The differences are increasing by 10 each time (90, 100, 110). The next difference should be 120, so 310+120=430 (option D). Alternatively, these could be adding prime numbers or following a different pattern, but the constant difference increase of 10 is the clearest pattern.

The series interleaves squares and cubes: squares at positions 1,3,5,7 (1,4,9,16) and cubes at positions 2,4,6,8 (1,8,?,64). The missing term is position 6, which should be 3³ = 27. Pattern: odd positions are n², even positions are n³.

The series alternates between two patterns: odd positions (3, 9, 15, ...) increase by 6, and even positions (2, 8, 14, ...) increase by 6. Position 7 continues the odd pattern: 15 + 6 = 21.

The series follows an alternating pattern: subtract 1, then add 3. Starting from 48: 48-1=47, 47+3=50, 50-1=49, so the next term is 49+3=52. Option B (58) would be the result if the pattern were consistently +2, which it is not.

The pattern involves multiplying by an increasing factor and adding: 6×2+1=13, 13×3-1=38, 38×3+15=129, 129×4+16=532, 532×5+15=2675. The missing term is 129.

The pattern is: multiply by increasing factor (0.5, 1, 1.5, 2, 2.5) and add the same factor. 17×0.5+0.5=9, 9×1+1=10, 10×1.5+1.5=16.5, 16.5×2+2=35, 35×2.5+2.5=90. The missing number is 10.

The series follows alternating multiplication: ×2.5, ×2, ×2.5, ×2, ×2.5, ×2. Verifying: 3×2.5=7.5, 7.5×2=15, 15×2.5=37.5, 37.5×2=75, 75×2.5=187.5 (not 167.5), 187.5×2=375. Therefore 167.5 is the wrong number.