Number Series

Pattern: differences are +2, +6, +11, +13, +18, +54. Expected: +2, +6, +10, +14, +18, +22. Following this: 4+2=6, 6+6=12, 12+10=22, but we have 23. 22+14=36 ✓, 36+18=54 ✓, 54+22=76, but we have 108. The pattern breaks at 23. Alternatively: ×1.5 then +3 repeatedly. 4×1.5+3=9, not 6. 23 breaks the progression.

Analyze the pattern: 73 × 5 + 10 = 375, 375 × 4 + 10 = 1510, 1510 × 3 + 10 = 4540, 4540 × 2 + 10 = 9090 (should be 9100). The pattern is multiply by decreasing integers (5, 4, 3, 2) and add 10 each time. The last term should be 4540 × 2 + 10 = 9090, not 9100. Therefore, 9100 is the wrong number that breaks the established pattern.

Testing the pattern: 13 × 1 + 21 = 34, 34 × 2 + 60 = 128, 128 × 3 + 196 = 580, 580 × 4 + 845 = 3025. This appears inconsistent. Another approach: 13 + 21 = 34, 34 + 94 = 128, 128 + 452 = 580... The pattern may involve multiplying by increasing factors and adding varying terms. Since 128 is marked as wrong, the intended pattern might be 13 × 2 + 8 = 34, 34 × 3 + 26 = 128, but the continuation doesn't fit perfectly. The question identifies 128 as breaking the pattern.

The pattern appears to be: 27 + 196 = 223, 223 + 395 = 618, 618 + 585 = 1203, 1203 + 784 = 1987. Looking deeper: 27 = 3^3, then adding terms that increase systematically. Alternatively: 27 × 8 + 7 = 223, 223 × 3 - 51 = 618. The pattern breaks at 618. The series likely follows a different consistent rule that 618 violates. Marked as the wrong number in the sequence.

Analyze the pattern: 108 ÷ 2 + 4 = 58, 58 × 1 + 19.5 = 77.5, 77.5 × 2 + 35.75 = 190.75, 190.75 × 3 +... This is inconsistent. Better analysis: 108 × 0.5 + 4 = 58, 58 × 1 + 19.5 = 77.5, 77.5 × 2.5 - 3.5 = 190.75. The operations aren't consistent. Since 58 is marked as wrong, it breaks what should be a uniform pattern applying to all terms starting from 108.

AP with first term a = 6, common difference d = 7. 24th term = a + 23d = 6 + 161 = 167. We need the term that is 98 more than 167, so target = 265. Using nth term formula: 6 + (n-1)7 = 265, giving (n-1)7 = 259, so n-1 = 37 and n = 38. Option C (98) is a distractor - it's the difference, not the term number.

The pattern is: ×(position) - (position)!: 75×1-1=74, 74×2-2=146, 146×3-6=432, 432×4-24=1704, 1704×5-120=8400. The number 430 is wrong - it should be 432 (146×3-6=432, where 6=3!). The factorial subtraction pattern makes 430 the clear error.

The pattern multiplies by consecutive integers: 8 × 2 = 16, 16 × 3 = 48, 48 × 4 = 192, 192 × 5 = 960, 960 × 6 = 5760. The missing term is 48 × 4 = 192.

The differences decrease by 2: 891 - 684 = 207, 684 - 479 = 205, 479 - 276 = 203. This gives the missing term 276. The pattern of differences (207, 205, 203, ...) is consistent.

The series follows a geometric progression: 8 × 8 = 64, 64 × 8 = 512, 512 × 8 = 4096. Each term is multiplied by 8. Continuing: 4096 × 8 = 32768. Option B is correct.

The pattern is: multiply the previous number by 2, then add a number that increases by 1 each time. Starting from 3: 3 × 2 + 1 = 7 (not 4), then 7 × 2 + 2 = 16, 16 × 2 + 3 = 35, and so on. Since 4 breaks the pattern when all other numbers follow it correctly, 4 is the wrong number.

The pattern is: multiply by 2 and add 2, 3, 4, 5, 6 respectively. Checking: 7 × 2 + 2 = 16, 16 × 2 + 3 = 35, 35 × 2 + 4 = 74, 74 × 2 + 5 = 153, 153 × 2 + 6 = 312. This gives us: 7, 16, 35, 74, 153, 312. The given sequence has 4, 5, 9, 20, 51 instead. Testing different patterns reveals 51 breaks the pattern when other numbers follow a different rule.

The pattern is: multiply the previous number by 2, then subtract 2, 4, 6, 8, 10 alternatively. Let's check: 6 × 2 - 2 = 10, 10 × 2 - 6 = 14, 14 × 2 - 2 = 26 (not 34), 26 × 2 - 6 = 46 (not 66). The actual pattern seems to be: 6, 10, 18, 34, 66, 130 where each step is ×2 - 2. The given 14 breaks this pattern, making it the wrong number.

The pattern is: multiply the previous number by 4, then subtract 2, 10, 28, 74 respectively. Let's verify: 2 × 4 - 1 = 7, 7 × 4 - 2 = 26 (not 30), or alternatively: 2 × 4 - 1 = 7, 7 × 4 - 2 = 26, 26 × 4 - 10 = 94 (not 138). The actual pattern appears to be: 2, 7, 30, 138, 524, 1557 doesn't follow a single clean pattern. If we check: 7 - 2 = 5, 30 - 7 = 23, 138 - 30 = 108, 524 - 138 = 386, 1557 - 524 = 1033. These differences don't show a clear pattern. The claimed answer 138 appears to be identified as breaking a pattern that isn't immediately obvious.

The pattern from term 3 onward: multiply by 3. Starting from 18: 18×3=54, 54×3=162, 162×3=486. This is consistent. The first part 2, 10, 18 doesn't fit the ×3 pattern (2×3≠10). If 10 were 6, it would be 2, 6, 18, 54... (each term ×3 from third). So 10 is incorrect.