Number Series

The pattern is: multiply by 4 and subtract 11, then multiply by 4 and subtract 7, then multiply by 4 and subtract 3. More systematically: (5 × 4) - 11 = 9, (9 × 4) - 7 = 25, (25 × 4) - 3 = 89. The subtracted numbers decrease by 4 each time (11, 7, 3). So next: (89 × 4) - (-1) = 356 - (-1) = 357, which doesn't match. Alternative pattern: terms are 1²+4, 3², 5², 9²+8, which doesn't work. The correct pattern is: (5 × 2) - 1 = 9, (9 × 3) - 2 = 25, (25 × 4) - 11 = 89, (89 × 5) - 100 = 345. The multiplier increases by 1, and subtracted terms follow 1, 2, 11, 100 (which are 1²-0, 2²-2, 3²+2, 10²+0). Therefore: 89 × 5 - 100 = 345.

The series should be cubes of prime numbers: 2³=8, 3³=27, 5³=125, 7³=343, 11³=1331, 13³=2197, 17³=4913. The given series is completely garbled. Among the options, 1331 (11³) is the only perfect cube of a prime, making it the correct choice for what should be in the series.

Pattern: ×7-7, ×6-7, ×5-7, ×4-7, ×3-7. Starting with 18: 18×7-7=119 (correct), 119×6-7=707 (not 708), 707×5-7=3528 (not 3534). The errors compound. By position 4, the correct value should be 3528, but 3534 is given, making 3534 the wrong term.

Each digit position follows a pattern. First digit: 4,5,6,7 → next is 8 (add 1). Second digit: 1,2,5,7 → pattern is adding consecutive odd numbers (1+1=2, 2+3=5, 5+2=7? No wait). Let me recalculate: 1→2 (+1), 2→5 (+3), 5→7 (+2), so 7→9 (+2). Third digit: 1→8 (+7), 8→9 (+1), 9→0 (+1 mod10), so 0→1 (+1). Fourth digit: 7→8 (+1), 8→9 (+1), 9→0 (+1 mod10), so 0→1 (+1). Therefore: 8191.

The sequence follows the pattern of triangular numbers where each term increases by consecutive integers: 1, 1+2=3, 3+3=6, 6+4=10, 10+5=15, 15+6=21, 21+7=28. The seventh term is 28.

The pattern follows adding consecutive integers with increasing increments: 7+5=12, 12+8=20, 20+11=31, 31+14=45. The increments increase by 3 each time: 5, 8, 11, 14. Following this pattern, the next increment is 17, so 45+17=62. However, checking the differences differently: 12-7=5, 20-12=8, 31-20=11, 45-31=14. These differences form an AP with common difference 3. Next difference would be 17, giving 45+17=62. None of the options match this. Let me reconsider: perhaps it's +5, +8, +11, +14, +16? That gives 61. Still no match. The pattern might be different. Actually, looking at it as n+5, n+8, n+11, n+14, n+13 seems inconsistent. Given the options, 58 is closest to a possible pattern continuation.

The series follows the pattern of adding consecutive increasing numbers: 1, 1+1=2, 2+4=6, 6+9=15, 15+16=31. The added numbers are squares: 1, 1+1²=2, 2+2²=6, 6+3²=15, 15+4²=31. Continuing this pattern: 31+5²=31+25=56. Alternatively, differences are: 1, 4, 9, 16 (squares of 1, 2, 3, 4). Next difference should be 25, giving 31+25=56.

Analyze the pattern: 12 × 2 + 3 = 27, 27 × 3 - 4 = 77, 77 × 4 + 5 = 313. The multipliers increase by 1 (2, 3, 4, 5), and the additives alternate between addition and subtraction with consecutive odd numbers (+3, -4, +5, -6). Following this pattern: 313 × 5 - 6 = 1565 - 6 = 1559.

The pattern involves cubes of consecutive integers from 9 downwards: -9³ = -729, then -729 + 2³ = -721, -721 + 5³ = -596 (since -721 + 125 = -596), -596 + 7³ = -253 (since -596 + 343 = -253). Following this pattern with 8³ = 512: -253 + 512 = 259. Since 259 is not among options A-D, option E is correct.

The pattern involves multiplication by fractions: 12 × 2/3 = 8, 8 × 3/2 = 12, 12 × 8/3 = 32. The numerators and denominators follow a pattern: numerators are 2, 3, 8, 9 and denominators are 3, 2, 3, 2. Following the pattern: 32 × 9/2 = 144. The fraction pattern alternates between denominators of 2 and 3, with numerators increasing.

The pattern alternates between addition and subtraction of consecutive odd numbers (prime sequence): -8 + 2 = -6, -6 - 3 = -9, -9 + 5 = -4, -4 - 7 = -11. The operations are +2, -3, +5, -7. Following this pattern with +11 (next odd number): -11 + 11 = 0. Since 0 is not among options A-D, option E is correct.

Analyze the differences between consecutive terms: 27 + 1 = 28, 28 + 4 = 32, 32 + 27 = 59. The added values are 1, 4, 27 which are 1¹, 2², 3³ respectively. Following this pattern, the next addition should be 4⁴ = 256. Therefore: 59 + 256 = 315.

The pattern alternates between two operations: first (x÷2+1), then (x+1). For 36: 36÷2+1=19, then 19+1=20, then 20÷2+1=11 (not shown). The series actually follows: 36→19 (÷2+1), 19→20 (+1), 20→31 (÷2+1), 31→63 (+1), 63→31.5 (÷2+1), 31.5→63 (+1)... Wait, let me recalculate: 36÷2+1=19, 19+1=20, 20÷2+1=11... This doesn't match. The actual pattern is: (÷2+1), (+1), (2x-9), (2x+1), (2x+32.5). For 158.5: (158.5×2)+32.5=317+32.5=349.5? No. Let me verify: 63×2.5-?=158.5. 63×2.5=157.5, so +1. The pattern involves doubling with different addends.

The series follows a pattern of cubes plus/minus 1: 2³-1=7, 3³+1=28, 4³-1=63, 5³+1=126, 6³-1=215, 7³+1=344. Each term alternates between (n³-1) and (n³+1) where n starts at 2 and increases by 1 each time. The missing term is 5³+1=125+1=126.

The sequence follows n²-1 pattern: 0=1²-1, 3=2²-1, 8=3²-1, 15=4²-1, 24=5²-1, ?=6²-1=35, 48=7²-1. Each term is one less than a perfect square. The missing number is 35 (6²-1).