Number Series

This is an interleaved series with two patterns. Positions 1,4,7,10: ?, 10, 5, 10 - pattern subtracts 5 then adds 5, so ? must be 15. Positions 2,5,8: 12, 6, 0 - subtracts 6 each time. Position 3,6,9: 18, 14, 10 - subtracts 4 each time. The missing number is 15.

The series follows a pattern where the difference between consecutive terms decreases by 5 each time: 163-125=38, 125-92=33, 92-64=28. The next difference should be 28-5=23, so 64-23=41. This is a decreasing arithmetic progression with a constant second-order difference.

Pattern: multiply by increasing odd numbers (3, 5, 7, 9, 11) and add the multiplier. 145x7+7=1018, not 6113. 3108 should be 1019x9+9=9190. 3108 is wrong.

Pattern: n² + n, then multiply by 2, 3, 4... 31+31=62x2=124; 43+43=86x3=258; 57+57=114x4=456; 73+73=146x5=730. Following this, 93 should produce 187x6=1122, not 93x6=558. 93 is wrong.

Pattern: +6, -8, +6, -8, +6, -8. Starting from 25: 25+6=31, 31-8=23, 23+6=29 (but 33 given), 29-8=21 (but 19 given). 33 breaks the pattern and is wrong.

Checking the pattern: 276+33=309, 309+35=344, 344+38=382, 382+38=420, 420+41=461. The additions should increase: 33, 35, 38, 38, 41. The jump 382→420 adds only 38, same as previous. If 382 were 380: 380+40=420, then 420+41=461 would fit better. 382 is the wrong number.

The differences between consecutive terms are 3, 6, 9, 12 - these increase by 3 each time. The next difference should be 15, so 358 + 15 = 373. This is a pattern of adding consecutive multiples of 3.

The pattern alternates between adding 1 and adding 3: 28+1=29, 29+3=32, 32+1=33, 33+3=36, 36+1=37. Following this alternating pattern, the next step is 37+3=40.

The pattern is: multiply by increasing integer (2,3,4,5,6) and subtract the square of that integer. 17×2-4=30, 30×3-9=81, 81×4-16=308, 308×5-25=1515. Therefore, 1515×6-36=9054. This combines both multiplication and subtraction in a progressive pattern.

This series follows the pattern where each term equals the sum of the two preceding terms: 8 + 9 = 17, 9 + 17 = 26, 17 + 26 = 43, 26 + 43 = 69, 43 + 69 = 112, 69 + 112 = 181. The term 70 should be 69 to maintain this Fibonacci-like pattern.

The pattern is: multiply position by increasing integers starting from 2, then subtract position number. Position 1: 1×2-1=1. Position 2: -3×3-2=-11 (but we have -3). Position 3: -4×4-3=-19 (but we have -4). Position 4: 1×5-4=1. Position 5: -4×6-5=-29 (but we have 18). Position 6: 18×7-6=120 (but we have 60). The last term should be 120, not 60.

Find the pattern in differences: 23-11=12, 43-23=20, 73-43=30, 115-73=42, 171-115=56. Second differences: 20-12=8, 30-20=10, 42-30=12, 56-42=14. Second differences increase by 2 each time. Next second difference = 16, so next first difference = 56+16=72, giving next term = 171+72=243. Option C is correct.

The series alternates between squares and cubes of consecutive integers: 1=1², 8=2³, 9=3², 64=4³, 25=5², 216=6³, ___=7²=49, 512=8³. The missing term is 7² = 49. Option B is correct.

The series shows consecutive cube numbers: 8=2³, 27=3³, 125=5³, 512=8³, 1728=12³. The bases are 2, 3, 5, 8, 12 - not consecutive. However, 2744=14³, 3375=15³, 4913=17³, 5832=18³. The pattern seems to skip cubes. Given 1728=12³, next should be 13³=2197 or 14³=2744, but 4913=17³ is marked correct. Pattern is unclear.

The series follows the pattern: n, n², 2n, (2n)², 4n, (4n)². Starting with 4: 4, 4²=16, 8, 8²=64, 16, 16²=256. The missing number is 16, which is 4×4.