Number Series

The series is 3, 6, 4, 7, 5, 8, ?, 9, 7. The pattern is +3, -2, +3, -2, +3, -2. 8-2 = 6.

The series is 5^1, 5^2, 5^3, 5^4, 5^5. The missing term is 5^3 = 125.

The series follows the pattern of multiplying by 4: 4*4=16, 16*4=64, 64*4=256, 256*4=1024, 1024*4=4096.

The series is a sequence of numbers where the last digit is removed sequentially: 234567, 23456, 2345, 234, 23.

The pattern alternates between subtracting 3 and adding 1: 17-3=14, 14+1=15, 15-3=12, 12+1=13, 13-3=10, 10+1=11.

The series follows the pattern of adding consecutive integers: 1+2=3, 3+3=6, 6+4=10, 10+5=15. The next term is 15+6=21.

The series follows a pattern of multiplying by increasing integers: 3*1=3, 3*2=6 (not 10), 6*6=36, 36*5=180, 180*6=1080, 1080*7=7560, 7560*8=60480. However, the pattern is actually 3*1=3, 3*2=6, 6*6=36, 36*5=180, 180*6=1080, 1080*7=7560, 7560*8=60480. Looking closer, the sequence is 3*1=3, 3*2=6, 6*6=36, 36*5=180, 180*6=1080. The sequence is 3, 6, 36, 180, 1080, 7560, 60480. The term 10 is clearly wrong.

The pattern is +23, -17, +23, +23... The sequence is 582, 605 (+23), 588 (-17), 611 (+23), 634 (+23). The term 634 breaks the alternating pattern.

The pattern is (previous number * 2) + 1. Specifically: 24*2+1=49, 49*2+1=99, 99*2+1=199, 199*2+1=399. Thus, 399*2+1 = 799.

The series alternates between two patterns: 53, 51, 49, 47 (subtracting 2) and 55, 57, 59 (adding 2). The next term in the first sequence is 47-2=45, and the next in the second is 59+2=61.

The pattern is multiplication: 6 * 2 = 12, 12 * 4 = 48, 48 * 6 = 288. The next term is 288 * 8 = 2304.

The series is an arithmetic progression with a=2 and d=2. The n-th term is a + (n-1)d. For n=15, term = 2 + (14*2) = 2 + 28 = 30.

The AP is 2, 7, 12... where a=2 and d=5. The 10th term is a + (10-1)d = 2 + 9*5 = 2 + 45 = 47.

This is an arithmetic progression with a=6, d=12, l=198. Formula: l = a + (n-1)d. 198 = 6 + (n-1)12. 192 = (n-1)12. 16 = n-1. n = 17.