The common difference is 5. The nth term of an arithmetic sequence is given by a_n = a + (n-1)d. Here, a = 5, d = 5, n = 10. So, a_10 = 5 + (10-1) * 5 = 5 + 45 = 50.

The nth term of a geometric series is given by a_n = a * r^(n-1). Here, a = 4, r = 3, n = 4. So, a_4 = 4 * 3^(4-1) = 4 * 27 = 108.

The nth term of an arithmetic series is given by a_n = a + (n-1)d. Here, a = 7, d = 2, n = 12. So, a_12 = 7 + (12-1) * 2 = 7 + 22 = 29.

The series consists of perfect squares. The nth term is n^2. Thus, the 7th term is 7^2 = 49.

Substituting n = 5 into the formula: a_5 = 2(5^2) + 3(5) - 1 = 2(25) + 15 - 1 = 50 + 15 - 1 = 64.

This is the Fibonacci sequence where each term is the sum of the two preceding ones. The next term is 3 + 5 = 8.

The differences between terms are 3, 5, 7, which increase by 2 each time. The next difference is 9, so 18 + 9 = 27.

This is a geometric series with a = 1 and r = 1/2. The sum of the first n terms is S_n = a(1 - r^n) / (1 - r). Here, S_5 = 1(1 - (1/2)^5) / (1 - 1/2) = 1(1 - 1/32) / (1/2) = 2(31/32) = 62/32 = 1.9375.

The differences are 3, 5, 7, 9, which increase by 2. The next difference is 11. The terms are 2, 5, 10, 17, 26, 37. The sum is 2 + 5 + 10 + 17 + 26 + 37 = 97.