Number Series

The series is 10, 9, 7, ?, 0. Differences: 10-9=1, 9-7=2. The next difference should be 3. 7-3=4. The next difference should be 4. 4-4=0. The pattern holds.

The series alternates between two patterns: 43, 42, 41, 40 (subtract 1) and 45, 46, 47 (add 1). The next term follows the first pattern, 41 - 1 = 40.

Differences: 0, 1, 4, 6, 19, 25. The pattern of differences is squares (0^2, 1^2, 2^2, 3^2, 4^2, 5^2). 49+0=49, 49+1=50, 50+4=54, 54+9=63, 63+16=79, 79+25=104. The term 60 should be 63.

The pattern is +2, +3, +2, +3, +2. 27 + 2 = 29.

The pattern is: 826 - 480 = 346; 480 - 346 = 134; 346 - 134 = 212. Each term is the difference of the two preceding terms.

The pattern is: 78 * 2 - 1 = 155; 155 * 2 - 1 = 309; 309 * 2 - 1 = 617; 617 * 2 - 1 = 1233.

Pattern: +3, *2, +3, *2, +3, *2. 5+3=8, 8*2=16, 16+3=19, 19*2=38, 38+3=41, 41*2=82.

The differences between consecutive terms are: 15-9=6, 26-15=11, 46-26=20, 83-46=37. The differences of these differences are: 11-6=5, 20-11=9, 37-20=17. The pattern of the second difference is 2*5-1=9, 2*9-1=17, 2*17-1=33. Adding 33 to 37 gives 70. Adding 70 to 83 gives 153.

The pattern is: 3*2+1=7, 7*2-1=13, 13*2+1=27, 27*2-1=53, 53*2+1=107.

The differences between consecutive terms are: 22-14=8, 37-22=15, 61-37=24, 96-61=35. The second differences are: 15-8=7, 24-15=9, 35-24=11. The next second difference should be 13. Thus, the next first difference is 35+13=48. The next term is 96+48=144.

The series consists of squares: 15^2=225, 13^2=169, 12^2=144, 10^2=100, 8^2=64. The next should be 6^2=36, but 48 is given.

Series: 2, 15, 54, 171, 522. Differences: 13, 39, 117, 351. These are powers of 3 times 13: 13*1, 13*3, 13*9, 13*27. Next difference = 13 * 81 = 1053. 522 + 1053 = 1575.

The pattern is alternating operations: 3 * 1.5 = 4.5; 4.5 / 4.5 = 1; 1 * 3.5 = 3.5; 3.5 / 3.5 = 1; 1 * 4.5 = 4.5; 4.5 / 1.5 = 3; 3 * 2.5 = 7.5. The missing term is 1.