Find the nth term of each sequence�(a) –1, 0, 7, 26, 63, f������������������������������������������������� [2](b) 24, 12, 6, 3, 1�5

(a) To find the nth term of the sequence -1, 0, 7, 26, 63, we first need to find the pattern or rule that the sequence follows.

Looking at the sequence, we can see that the difference between consecutive terms is increasing. This suggests that the sequence might be cubic.

Let's try to find the differences between consecutive terms:

0 - (-1) = 1 7 - 0 = 7 26 - 7 = 19 63 - 26 = 37

The differences are not constant, so let's try to find the second differences:

7 - 1 = 6 19 - 7 = 12 37 - 19 = 18

The second differences are also not constant, so let's try to find the third differences:

12 - 6 = 6 18 - 12 = 6

The third differences are constant, which confirms that the sequence is cubic.

The nth term of a cubic sequence is of the form an^3 + bn^2 + cn + d.

Given that the third difference is 6, the coefficient a of n^3 is 6/6 = 1.

To find the coefficients b, c, and d, we can substitute the first four terms of the sequence into the formula and solve the resulting system of equations.

Doing this, we find that the nth term of the sequence is n^3 - 2n + 1.

(b) To find the nth term of the sequence 24, 12, 6, 3, 1.5, we first need to find the pattern or rule that the sequence follows.

Looking at the sequence, we can see that each term is half of the previous term. This suggests that the sequence is geometric.

The nth term of a geometric sequence is of the form ar^(n-1), where a is the first term and r is the common ratio.

In this case, a = 24 and r = 1/2.

Therefore, the nth term of the sequence is 24*(1/2)^(n-1).