### Home > PC3 > Chapter 12 > Lesson 12.1.2 > Problem12-28

12-28.

As stated in the preceding Math Notes box, in a recursive sequence, each term is defined in terms of one or two of the terms immediately preceding. Practice this idea by using the first term and the recursive definition to write the next four terms of each of these sequences. Part (a) is partially done for you

1. $x_{n+1} = 4x_n − 10$; $x_{1} = 5$

$x_4 = 4(30) − 10$          $x_5 = 4(4(30) − 10) − 10$

2. $y_{n+1} = (y_n)^2 − 4$$y_1 = 0$

$y_{2} = 0^{2} − 4\\y_{3} = \left(0^{2} − 4\right)^{2} − 4\\y_{4} = ?\\y_{5} = ?$

3. $z_{n+1} =\frac { 1 } { z _ { n } }$; $z_{1} = 4$

$z_2=\frac{1}{4}$

$z_3=\frac{1}{\frac{1}{4}}$

4. $w_{n+2} = w_{n+1} · w_n$; $w_{1} = 3$, $w_{2} = 5$

$w_{3} = w_{2} · w_{1} = 3 · 5$