Question

A) Xn+1=2Xn+1 x1=-5b) Xn+1= 3Xn+Xn-1 +2 X1=1 X2= 2

Answer 1

Ответ:

Пошаговое объяснение:

A) Xn+1=2Xn+1x1=-5

Xn-2Xn-1x=5-1+1

Xn=5/1

Xn=5

B) Xn+1=3Xn+Xn-1+2x1=1x2=2

Xn-3Xn-Xn-2x-1x=-2-2

3Xn-3x=-4

Answer 2

To solve the given recursive sequences, we'll use the provided initial values to calculate the terms of the sequences.

A) Xn+1 = 2Xn + 1, X1 = -5

Let's calculate the first few terms of the sequence:

X1 = -5 (given) X2 = 2 * X1 + 1 = 2 * (-5) + 1 = -9 X3 = 2 * X2 + 1 = 2 * (-9) + 1 = -17 X4 = 2 * X3 + 1 = 2 * (-17) + 1 = -33 ...

The first few terms of the sequence are: -5, -9, -17, -33, ...

B) Xn+1 = 3Xn + Xn-1 + 2, X1 = 1, X2 = 2

Let's calculate the first few terms of the sequence:

X1 = 1 (given) X2 = 2 (given) X3 = 3 * X2 + X1 + 2 = 3 * 2 + 1 + 2 = 9 X4 = 3 * X3 + X2 + 2 = 3 * 9 + 2 + 2 = 31 X5 = 3 * X4 + X3 + 2 = 3 * 31 + 9 + 2 = 104 ...

The first few terms of the sequence are: 1, 2, 9, 31, 104, ...

Keep in mind that these sequences might not have a simple closed-form expression. They are defined by their recursive formulas, and the terms can become quite large or complex as the index (n) increases.