Number Series

The pattern is: aₙ₊₁ = aₙ×(n+1) + (n+1). So 88×1+1=89, 89×2+2=180, 180×3+3=543, 543×4+4=2176. The number 541 breaks this—it should be 543.

The series consists of squares of consecutive odd numbers: 27²=729, 29²=841, 31²=961, 33²=1089, 35²=1225. The number 1090 is incorrect — it should be 1089 (which is 33²) to maintain the pattern.

The series follows the pattern: ×3−6, ×4−7, ×5−8, ×6−9, ×7−10. Starting with 12: 12×3−6=30, 30×4−7=113, 113×5−8=557, 557×6−9=3333, and 3333×7−10=23321 (which matches the last term).

Series: 16, 22, 30, 45, 52, 66. Differences: +6, +8, +15, +7, +14. If 45 were correct (say 38), we'd have +6, +8, +12, +14, +16 - a pattern of increasing even numbers. But with 45, the pattern breaks: +6, +8, +15, +7, +14 has no consistent rule. 45 is the wrong term that disrupts the pattern.

Series: 5, 10, 40, 80, 320, 550, 2560. Pattern: ×2, ×4, ×2, ×4, ×?, ×4. Following the pattern, 550 should be 320×4 = 1280 (since previous was ×4). But we have 550 which breaks the ×2,×4 alternating pattern. 550 is the wrong term.

The series 6, 14, 31, 64, 137, 280 should follow the pattern: ×2+2, ×2+3, ×2+4, ×2+5, ×2+6. Checking: 6×2+2=14✓, 14×2+3=31✓, 31×2+4=66 (not 64), 64×2+5=133 (not 137), 137×2+6=280✓. The number 64 breaks the pattern - it should be 66.

The series has two interleaved patterns. Odd positions: 46, 47, 49, ? (differences: +1, +2, +3 → 49+3=52). Even positions: 50, 55, 61 (differences: +5, +6). The missing term is at position 7 (odd), so we add 3 to 49 to get 52.

The pattern is adding 0.8 to each term: 1.5 + 0.8 = 2.3, 2.3 + 0.8 = 3.1, 3.1 + 0.8 = 3.9, 3.9 + 0.8 = 4.7. The next term is 4.7. This is a simple arithmetic progression with a constant difference of 0.8.

The pattern is subtracting consecutive decreasing squares: 109 - 35 = 74, 74 - 28 = 46, 46 - 21 = 25, 25 - 14 = 11. The differences are 35, 28, 21, 14 (decreasing by 7). Next difference = 14 - 7 = 7. So: 11 - 7 = 4.

This series follows a pattern involving cubes: each term is derived from the previous term through multiplication by an increasing factor and adding/subtracting values related to cubes. The pattern is: ×1 - 1³, ×2 - 2³, ×3 - 3³, ×4 + 4³, ×5 - 5³. 438 breaks this pattern as it should be 445 (93 × 4 + 4³ = 372 + 64 = 436, not 438).

The pattern is: (28-3)×5=25, (25-5)×10=250 (not 70), (250-7)×15=3645 (not 336), (3645-9)×20=72720 (not 2340). The correct number at position 3 should be 250, not 70. Alternatively, using the pattern (n-3)×5: 28×5=140, 25×5=125, 70×5=350, 336×5=1680, 2340×5=11700 - these don't show a clear progression either way, but 70 is clearly the anomaly that breaks the emerging pattern.

The pattern is: multiply by increasing integers and add the same integer. 124×2+2=250, 250×3+3=753, 753×4+4=3016, 3016×5+5=15085. The next should be 15085×6+6=90516, not 90518. The last number breaks the pattern.

The pattern involves subtracting consecutive squares of prime numbers: 23² = 529, 19² = 361, 17² = 289, 13² = 169, 11² = 121. Working backwards: 2500-529=1971, 1971-361=1610, 1610-289=1321, 1321-169=1152, but 1152-52=1100 instead of 1152-121=1031. The last term breaks the pattern, so 1100 is incorrect.

The pattern multiplies each term by 3: 12.35×3=37.05, 37.05×3=111.15, 111.15×3=333.45, 333.45×3=1000.35. The last term should be 1000.35, not 1002.35. The slight difference (1002.35 vs 1000.35) indicates 1002.35 is the wrong number.

The pattern adds consecutive odd numbers starting from 25: 1253+25=1278, 1278+34=1312 (but 34 is not odd), 1312+40=1352, 1352+49=1401, 1401+57=1458. Looking more carefully: differences are 25, 34, 40, 49, 57 - which follow a pattern where the difference increases by 9, 6, 9, 8... actually 1312 breaks the expected pattern. The correct difference between 1278 and next should maintain the pattern. 1312 is the wrong term.