Number Series

The series follows the pattern n^3 - 1: 2^3-1=7, 3^3-1=26 (not 28), 4^3-1=63, 5^3-1=124, 6^3-1=215, 7^3-1=342, 8^3-1=511. The wrong number is 28.

n-th term = n + 2^(n-1). 5th term = 5 + 2^4 = 5 + 16 = 21. 6th term = 6 + 2^5 = 6 + 32 = 38. Difference = 38 - 21 = 17.

Arithmetic sequence: a = 5, d = 3. Formula for n-th term: a_n = a + (n-1)d. a_17 = 5 + (17-1)3 = 5 + 16*3 = 5 + 48 = 53.

This is an arithmetic sequence with first term a = 1 and common difference d = -3. The n-th term is given by a + (n-1)d; for n = 12, the term is 1 + (11 * -3) = 1 - 33 = -32.

This is an arithmetic sequence with first term a = -5 and common difference d = 3. The n-th term is a + (n-1)d. For n=21, term = -5 + (20 * 3) = -5 + 60 = 55.

The series is arithmetic with a = 4 and d = 5. The 50th term is a + (n-1)d = 4 + (49 * 5) = 4 + 245 = 249.

The differences between consecutive terms of the sequence are 5, 6, 7, and 8. Following this pattern, the next difference must be 9. Adding 9 to the last term, 29, gives the next term as 38.

The sequence is 1/(1*2), 1/(2*3), 1/(3*4), 1/(4*5). The next term is 1/(5*6) = 1/30.

The sequence is the Fibonacci sequence: 1, 1, 2, 3, 5, 8, 13, 21. The 8th term is 21.

This is an arithmetic progression with a = 5 and d = 3. The 10th term = a + (n-1)d = 5 + (9 * 3) = 5 + 27 = 32.