Number Series

This series follows a pattern of multiplying by 2 and alternately adding and subtracting 1. Specifically: 9 × 2 + 1 = 19, 19 × 2 - 1 = 37, 37 × 2 + 1 = 75, 75 × 2 - 1 = 149. Following this pattern, 149 × 2 + 1 = 299.

This series follows a simple pattern of dividing each term by 2 to get the next term. Starting with 2, we get: 2 ÷ 2 = 1, 1 ÷ 2 = 1/2, 1/2 ÷ 2 = 1/4, and 1/4 ÷ 2 = 1/8. This is a geometric progression with a common ratio of 1/2.

Find the pattern in differences: 132-126=6, 142-132=10, 148-142=6. The differences alternate between 6 and 10. Next difference = 10, so 148+10=158.

This is a Fibonacci series where each term (after the first two) equals the sum of the two preceding terms. 0+1=1, 1+1=2, 1+2=3, 2+3=5, 3+5=8, 5+8=13. Therefore, the missing term after 13 is 8+13=21. Verification: 21+13=34, which matches the next given term.

The pattern is n² + 1: 0²+1=1, 1²+1=2, 2²+1=5, 3²+1=10, 4²+1=17, 5²+1=26, 6²+1=37, 7²+1=50, 8²+1=65, 9²+1=82, 10²+1=101. Wait, this doesn't match. Let me recalculate: The actual pattern is odd numbers added to positions: 1+(2×0)=1, 1+(2×2.5)=6, 1+(2×7)=15, 1+(2×13.5)=28, 1+(2×22)=45. The correct pattern is (n²-1): for n=2:4-1=3 doesn't match. The working pattern is adding consecutive odd numbers starting from 1: 1+5=6, 6+9=15, 15+13=28, 28+17=45, 45+19=64 doesn't match 66. Actually: 1 (+5)=6 (+9)=15 (+13)=28 (+17)=45 (+21)=66 (+25)=91. The missing term is 28.

The series pattern is 6³-0=216, 5³-?=?, 4³-56=120-56=64 (not 72), 3³-27=27, 2³-8=0. Alternatively: 216, 216-53=163, 163-43=120, 120-48=72 (break), 72-48=24. The pattern is imperfect. However, 163 is the most clearly wrong - it should be 125 (5³) to complete a perfect cube series 6³,5³,4³,3³,2³.

The pattern is 11, 101, 1001, 10001, 100001, 1000001 (increasing zeros). The first bracket has 10001 (should be 10001 with 4 zeros), which is correct. The second bracket has 10000001 (should be 1000001 with 6 zeros), which is incorrect.

The pattern is: (previous × 1) + 0, (previous × 2) + 3, (previous × 3) + 5, (previous × 4) + 7, (previous × 5) + 9. Following this pattern: 2, 2×2+3=7, 7×3+5=26 (not 23), 26×4+7=111 (not 87), 111×5+9=564 (not 342). The number 23 should be 26 to fit the pattern.

The pattern is 2³-1=7≈5, 5³-3=122≠9, 9³-5=724≠42. The series follows a pattern of cube of natural numbers minus consecutive odd numbers (1, 3, 5, 7, 9). Applying this: 2³-1=7, 5³-3=122, 9³-5=724, 42³-7=74061, 98³-9=941183. The last term 234 doesn't fit this pattern.

In the series 12, 7, 9, 22, 96, 780, checking the pattern: 12-7=5, 7×9=63, 22+96=118. The last term 780 is incorrect because if we follow the pattern of (previous-2)×current, we get (96-2)×22=2072, not 780. The pattern breaks at the final term.

The pattern is: divide by 20, then divide by 2.5, alternating. 5000/20 = 250, but 250 should be followed by 250/2.5 = 100. Checking: 100/20 = 5 (not 30), 5/2.5 = 2 (not 12), etc. The pattern breaks. The correct term at position 2 should be 5 (not 250), giving the sequence: 5000, 5, 100, 30, 12, 6, 3.6. The claimed answer (B: 250) is correct - 250 is the wrong term.

The series follows an alternating pattern: subtract 8, add 15, subtract 15, add 15, subtract 15, add 15. Checking: 120 - 8 = 112, but the second term is 128. So 128 breaks the pattern. If the pattern were -8, +15 starting with 120, we'd get: 120, 112, 127, 119, 134... This doesn't match. Actually, the pattern is: -8, +3 repeated but 128 should be 112 to maintain consistency. The claimed answer (A: 128) is correct - 128 is the wrong term.

The pattern is division by consecutive integers 6, 5, 4, 3, 2, 1. Checking: 1440/6=240, 240/5=48, 48/4=12, 12/3=4, 4/2=2, 2/1=2. The term 3 breaks this pattern - it should be 2 instead of 3, or the sequence after 4 should be 4/2=2 not 3. Also, if 3 were correct, the next term should be 3/1.5=2 which doesn't fit the integer pattern.

The pattern is: previous term × (n+3) - (n-1) where n increases by 2 each time, starting with n=2. 13×5-3=62, 62×7-5=429 (not 355), 429×9-7=3854 (not 1416), etc. The term 62 is wrong because the actual pattern is ×(4+2n)-(?). Better pattern: 13×5-3=62, then it should be 62×7-5=429. Since 355 is given, check if 62 itself is wrong. If we start with 62, next should be 62×6-17=355. But then 355×4-4=1416. The multipliers and subtractions are inconsistent. The correct pattern starting from 13 would be: 13×5-3=62, 62×7-5=429, 429×9-7=3854... So 62 is the wrong term.

The pattern is: subtract consecutive odd numbers starting from 1, but increasing by odd number differences. The differences are: 165-163=2, 163-158=5, 158-148=10, 148-140=8, 140-105=35, 105-68=37. The pattern 2, 5, 10, 17, 26, 37 (each difference increases by consecutive odd numbers 3, 5, 7, 9, 11) gives: 165-2=163, 163-5=158, 158-10=148, 148-17=131, 131-26=105, 105-37=68. The term 140 should be 131.