Number Series

Square number sequence: 1, 4, 9, 16, 25, 36, 49, 64, 81. The 9th term is 81. 9 times the 9th term = 9 * 81 = 729.

The n-th term is 5n + 4. For n=1, term is 5(1)+4 = 9. For n=2, term is 5(2)+4 = 14.

This is an arithmetic progression with first term a=3 and common difference d=4. The n-th term is a + (n-1)d. For n=20, term = 3 + (19 * 4) = 3 + 76 = 79.

For n=1, 2(1)+7 = 9. For n=2, 2(2)+7 = 11. For n=3, 2(3)+7 = 13.

This is an arithmetic progression with the first term a = 44 and common difference d = 4. The n-th term is calculated as a + (n-1)d; for n = 20, this is 44 + (19 * 4) = 44 + 76 = 120.

For an arithmetic sequence, a + 4d = 15 and a + 9d = 20. Subtracting the equations gives 5d = 5, so d = 1. Substituting d = 1 into the first equation, a + 4 = 15, so a = 11.

Pattern: x*1-1, x*3+0, x*4-2... The series is 4, 3, 9, 34, 96, 219, 435. Checking differences: -1, 6, 25, 62, 123, 216. These are (n^3-2). 435 is the outlier.

The series is two interleaved series: 2, 6, 12, (?) and 30, 20, 12. The first series follows n(n+1) for n=1, 2, 3, 4: 1*2=2, 2*3=6, 3*4=12, 4*5=20.

The pattern is: 7*2+1=15, 15*2-2=28, 28*2+3=59, 59*2-4=114, 114*2+5=233.

The series follows a pattern of alternating subtraction and addition: 89 - 11 = 78, 78 + 8 = 86, 86 - 6 = 80, 80 + 5 = 85, 85 - 3 = 82, 82 + 1 = 83. The pattern of differences is -11, +8, -6, +5, -3, +1. This is inconsistent. Checking the series 89, 78, 87, 80, 85, 82, 83, the differences are -11, +9, -7, +5, -3, +1. The term 86 is the wrong one.

The series is 3, 5, 7, ?, 13, 17. These are consecutive prime numbers. The prime after 7 is 11.

The pattern is multiplication by increasing integers: 2*2=4, 4*3=12, 12*4=48, 48*5=240.

The series follows an arithmetic progression with a common difference of 3. Adding 3 to the previous term 15 gives 18.

The series follows an arithmetic progression with a common difference of 0.5. The sequence is 0.5, 1.0, 1.5, 2.0, 2.5, 3.0.