Substituting n = 7 into the formula gives a_7 = 3(7) + 1 = 21 + 1 = 22.

Substituting n = 7 into the formula gives a_7 = 3(7) + 2 = 21 + 2 = 23.

The 3rd term is given by ar^2. So, 12 = a(2^2) => a = 12/4 = 3.

Let the first term be a and the common difference be d. Then, a + 2d = 12 and a + 6d = 24. Solving these gives d = 3.

The number of terms n can be calculated using the formula: n = (last - first) / difference + 1. Here, n = (50 - 10) / 5 + 1 = 9.

The nth term of an arithmetic sequence is given by a + (n-1)d. Here, a = 5, d = 3, n = 10. So, 5 + (10-1)3 = 32.

Substituting n = 7 into the formula gives a_7 = 5*7 - 3 = 35 - 3 = 32.

The 4th term is 4^2 + 4 = 16 + 4 = 20.

A constant ratio of consecutive terms indicates that the series is exponential.

The constant ratio of consecutive terms in a geometric series is called the common ratio.

The constant ratio of consecutive terms in a geometric series is called the common ratio.

Using the formula for the sum of a geometric series, S_n = a(1 - r^n) / (1 - r), we can solve for r. Here, S_5 = 1(1 - r^5) / (1 - r) = 31, leading to r = 3.

The common difference can be found by calculating S_n - S_(n-1). Here, S_n = 3n^2 + 2n and S_(n-1) = 3(n-1)^2 + 2(n-1). The difference simplifies to 4.

The common difference can be found by calculating S_n - S_(n-1). This gives the common difference as 5.

The 10th term can be found using T_n = S_n - S_(n-1). Here, S_10 = 5(10) + 3 = 53 and S_9 = 5(9) + 3 = 48. Thus, T_10 = 53 - 48 = 5.

The 4th term can be found using T_n = S_n - S_(n-1). Here, S_4 = 5(4) + 3 = 23 and S_3 = 5(3) + 3 = 18. Thus, T_4 = 23 - 18 = 5.

'd' represents the common difference in an arithmetic series.

'a' represents the first term of the arithmetic series.

The nth term of a geometric series is given by ar^(n-1). Here, a = 4, r = 2, n = 6. So, 4 * 2^(6-1) = 4 * 32 = 128.

The sum of the first n terms of a geometric series is a(1 - r^n) / (1 - r). Here, a = 4, r = 2, n = 5. So, 4(1 - 2^5) / (1 - 2) = 4(1 - 32) / -1 = 124.

a_7 = 3(7) + 1 = 21 + 1 = 22.

Substituting n = 7 into the formula gives a_7 = 3(7) + 2 = 21 + 2 = 23.

Substituting n = 5 gives a_5 = 5^2 + 5 = 25 + 5 = 30.

Substituting n = 7 into the formula gives a_7 = 3(7) + 2 = 21 + 2 = 23.

The sequence is 1, 2, 4, 8, 16, 32, 64, 128. The 8th term is 128.

The sequence is 1, 2, 4, 8, 16, 32, 64. The 6th term is 64.

The first four terms are 1^2, 2^2, 3^2, 4^2 which are 1, 4, 9, 16. Their sum is 30.

The sequence is 2, 3, 5, 8, 13. The fifth term is 13.

The sequence is 2, 3, 5, 8, 13. The 5th term is 13.

The series is 1, 2, 4, 8, 16, 32. The 6th term is 32.