Number Series

The pattern is: next term = previous term × n + 2.5, where n increases by 1 (1.25, 2, 3, 4, 5...). 10×1.25=12.5, 12.5×2+2.5=27.5, 27.5×3+2.5=85, 85×4+2.5=342.5. Then 342.5×5+2.5=1715, not 1725.

Pattern: 2×1.5=3, 3×2=6, 6×3=18, 18×4.5=81, 81×6=486, 486×7.5=3645, 3645×9=32805. The multiplier increases by 0.5, then 1, then 1.5, then 1.5, then 1.5... Wait, let me verify: 2×1.5=3, 3×2=6, 6×3=18, 18×6=108 (not 109), 108×18=1944, 1944×108=209952. The pattern is: multiply by 1.5, 2, 3, 6, 18, 108 (each multiplier is previous multiplier × something). 109 breaks the pattern.

Pattern: differences are 4, 10, 22, 46, 92, 192. Each difference roughly doubles and adds 2. But 176 is wrong: it should be 178 (84 + 94, where 92+2=94). Let me verify: 2, 6(×2+2), 16(×2+4), 38(×2+6), 84(×2+8), 176(×2+10, should be 178), 368. The pattern is ×2+(2,4,6,8,10,12). 176 should be 178.

The series increases by 7.3 each time: 7 + 7.3 = 14.7, 14.7 + 7.3 = 22.4, 22.4 + 7.3 = 30.1. Continuing: 30.1 + 7.3 = 37.8.

This series follows the pattern: multiply by 2 and subtract 1. 113×2-1=225, 225×2-1=449, 449×2-1=897, 897×2-1=1793. Therefore the missing term is 897. This is a multiplication and subtraction series.

Pattern: differences are 1, 9, 25, 49, 64, 138. These should be squares of odd numbers: 1², 3², 5², 7², 9². But after 90 (should be 90+81=171), we get 154 instead of expected 171, breaking the pattern.

The series follows the pattern: each term (from 2nd onward) = previous term × 3^1 - 9.5, × 3^2 - 28.5, × 3^3 - 85.5, and so on, where the subtrahend triples each time (× 3). Applying this: 2.5 = 4 - 1.5; 3.5 = 2.5 × 3 - 4; 6.5 ≠ 3.5 × 3 - 8.5 (should be 2); 15.5 = 2 × 3 - 0.5. The number 6.5 breaks the pattern.

The series follows: 484 ÷ 2 - 2 = 240, 240 ÷ 2 - 2 = 118, not 120. The pattern is divide by 2 and subtract 2. Checking: 240 ÷ 2 - 2 = 118 (given 120), 118 ÷ 2 - 2 = 57 (works), 57 ÷ 2 - 2 = 26.5 (works), 26.5 ÷ 2 - 2 = 11.25 (works). Therefore 120 is the wrong number.

The pattern follows subtraction of squares in descending order: 15² (225), 12² (144), 9² (81), 6² (36), 3² (9). Checking the series: 4553 - 225 = 4328 ✓; 4328 - 144 = 4184 ✓; 4184 - 81 = 4103 (should be 4103, not 4113); 4113 breaks the pattern. If we continue: 4103 - 36 = 4067 ✓; 4067 - 9 = 4058 ✓. Therefore, 4113 is the wrong number.

The pattern is: divide by 4.5, then divide by 3.5, then divide by 2.5, then divide by 1.5, then divide by 0.5. Checking: 7087.5 ÷ 4.5 = 1575 ✓; 1575 ÷ 3.5 = 450 ✓; 450 ÷ 2.5 = 180 ✓; 180 ÷ 1.5 = 120 ✓; 120 ÷ 0.5 = 240 ✓. The number 1578 in the options doesn't appear in this correct series, making it the wrong number to identify.

The pattern alternates between multiplication and addition operations. Starting with 27: 27 × 7 = 189 ✓; 189 + 12 = 201 ✓; 201 × 7 = 1407 (not 1372). The number 201 breaks the pattern because 201 × 7 = 1407, but we have 1372. If we had 201 × 7 = 1407, then 1407 + 12 = 1419 (not 1379), 1419 × 7 = 9933 (not 9653). Actually checking: 27 × 7 = 189, 189 + 12 = 201, 201 × 7 = 1407, 1407 + 12 = 1419, 1419 × 7 = 9933. The given number 1372 = 196 × 7, so 196 should have been there instead of 201. Thus 201 is the wrong number.

The pattern follows: multiply by increasing fractions and then add 1. Specifically: 12 × 1/2 + 1 = 7 (not 12), but looking at the actual sequence: 12 to 12 (×1), 12 to 18 (×1.5), 18 to 45 (×2.5), 45 to 180 (×4). The multipliers increase by 0.5, then 1.0, then 1.5. Therefore: 45 × 4 = 180. Options 124, 140, and 135 don't fit this pattern.

The pattern works backwards with digit operations: 121→1+2+1=4, then 4^2=16; 16→1+6=7, then 7^2=49; 49→4+9=13, then 13^2=169; continuing 169→1+6+9=16→256→...→29→2+9=11→121. Going forward: 1961→1+9+6+1=17→17^2=289→2+8+9=19→19^2=361→... ultimately reaching 489.

Pattern: ×3, ×3, ×3, ×3. Starting from 18: 18, 54, 162, 486, 1458. But the series shows 2, 10, 18... The term 10 breaks the geometric progression. If it were 6 instead of 10, the pattern 6, 18, 54, 162, 486, 1458 would work (each ×3). Therefore 10 is the wrong number.

Pattern: differences are +12, +15, +18, +22, +23, +27. Expected: +12, +15, +18, +21, +24, +27. With +21 at position 4: 57+21=78, then 78+24=102, 102+27=129. The actual term is 79 instead of 78, so 79 is wrong. Or using n²+(n+10): 12=1²+11, 24=3²+15, 39=5²+14(no), 57=7²+8... 79=8²+15, but pattern breaks.