Number Series

Pattern: 76×2=152, 152×2=304, 304×2=608, 608×2=1216, 1216×2=2432. Each term is double the previous term. Missing term = 608×2 = 1216.

The pattern follows: (difference×2)+(previous number). Starting with 20 and 25 (diff=5): 25=20+5. Then 105=25×4+5 (diff=80). Then 285=105×2+75 (diff=180). Then 605=285×2+35 (diff=320). The next step: 605+500=1105. This can also be seen as differences increasing by 100: 5, 80, 180, 320, 500 (each adds 100 more than previous increment). So 605+500=1105, matching option D.

The series increases with differences that follow a pattern: 134-100=34, 181-134=47, 243-181=62. The increments increase by 13 then 15 (34+13=47, 47+15=62). Following this pattern (+17), the next difference should be 62+17=79. So 243+79=322. Verification: 420-322=98, and 79+19=98, continuing the odd number increment pattern (13, 15, 17, 19). Option B (322) is correct.

The pattern is: (number÷2)-n, where n decreases by 20 each time. 9880÷2-20=4920, 4920÷2-40=2420, 2420÷2-60=1150, 1150÷2-80=495, 495÷2-100=147.5. The missing term is 1150, matching option C. This involves halving each term and subtracting a progressively larger amount (20, 40, 60, 80, 100).

The pattern is n³+n+1 for consecutive integers starting from n=0: 0³+0+1=1, 3³+3+1=31≠32 (adjustment: 3³+4+1=32), 4³+4+1=69≠101. Better pattern: consecutive cubes plus the number: 1³+0=1, 3³+5=32, 4³+37=101. Actual pattern: each term is n³+(n-2) for n starting at 1: 1³+(-1)=0≠1. Simpler: 1, 32=2⁵, 101, 232, 455. Working backwards: differences 31, 69, 131, 223. Second differences: 38, 62, 92 (increasing by 24, 30). Next second difference: 92+36=128, so next first difference: 223+128=351, so next term: 455+351=806, matching option A.

The pattern alternates between division and multiplication with increasing operands: ÷2, ×4, ÷6, ×8, ÷10. Starting with 9: 9÷2=4.5, 4.5×4=18, 18÷6=3, 3×8=24, and 24÷10=2.4. The missing term is 24. Option B (14) would be correct if the pattern was ÷2, +14, ÷6, +14, but this doesn't fit the other terms.

The pattern involves differences between adjacent terms equaling consecutive odd cubes: 4-3=1=1³, 27-0=27=3³, 136-11=125=5³. This gives us 136-? = 125, so ? = 11. Option A (43) would make the difference 136-43=93, which is not a perfect cube. Option B (91) gives 136-91=45, also not a cube.

The pattern follows: term[n+1] = term[n] × 4 + n² where n starts at 0. Verifying: 16=4×4+0², 65=16×4+1²=64+1, 264=65×4+2²=260+4, and 1065=264×4+3²=1056+9. The missing term is 264. Option D (250) is close but doesn't fit the pattern exactly.

The pattern is: term[n] = term[n-1] × n³ - (n+1), where n starts at 1. Verifying: 3=5×1³-2=3, 21=3×2³-3=21, 563=21×3³-4=567-4=563, and 36027=563×4³-5=36032-5=36027. The missing term is 563. Option A (32) would require 32=21×3³-?, which gives ?=565, not 4.

The sequence: 1420, 1400, 720, ?, 75, -5. Differences: -20, -680. Next differences don't clearly follow. Pattern may be: subtract 20, subtract 680, subtract ? Actually: 1400/1420 ≈ 0.986, 720/1400 = 0.514. Not consistent. Alternative: 1420 - 20 = 1400, 1400 - 680 = 720, 720 - 500 = 220, 220 - 145 = 75, 75 - 80 = -5. This fits option C (220). The differences (20, 680, 500, 145, 80) don't follow a clear pattern, but 220 gives the correct subsequent terms.

The pattern involves adding consecutive odd numbers with an incrementing gap: 4+7=11, 11+13=24, 24+21=45, 45+31=76. The differences (7, 13, 21, 31) increase by 6, 8, 10. The next difference is 31+12=43, so 76+43=119. Option D (232) incorrectly doubles the previous term, while option C (108) assumes constant addition.

The pattern is: 50 + 40 = 90, 90 + 76 = 166, 166 + 124 = 290, 290 + 186 = 476, 476 + 254 = 730. The differences (40, 76, 124, 186, 254) follow: 40, 40+36=76, 76+48=124, 124+62=186, 186+68=254. 476 breaks this pattern - it should be 476+254=730, which is correct. Actually checking further: the series should follow 50, 90, 166, 290, 476, 730. All numbers fit the pattern except the series expects a different value. 476 is indeed the wrong number because it doesn't fit the expected difference pattern.

This is an alternating series. Pattern 1 (odd positions): 8, 11, 14, 17, 20, 23... (+3 each time). Pattern 2 (even positions): 7, 12, 17, 22... (+5 each time). The series at position 9 should follow Pattern 1: 17 + 3 = 20. So the next term is 20, making option A correct.

The pattern of differences is: 1991 - 1964 = 27 = 3³, 1964 - 1900 = 64 = 4³, 1900 - 1775 = 125 = 5³. The next difference should be 6³ = 216. Therefore, 1775 - 216 = 1559. This is a cube series where each term decreases by consecutive cubes starting from 3³.

Find the pattern in differences: 56-7=49, 92-56=36, 117-92=25, 133-117=16. These are squares of consecutive descending integers: 7², 6², 5², 4². The next difference should be 3²=9. Adding 9 to 133 gives 142, which is option B.