Question

1.)Given the recursive definition LaTeX: a_{n+1}=2\cdot a_n+1a n + 1 = 2 ⋅ a n + 1, and that LaTeX: a_1=1a 1 = 1, find LaTeX: a_{10}a 10
Group of answer choices


2.)Given the explicit definition: LaTeX: t_n=n^2-2nt n = n 2 − 2 n, find LaTeX: t_4

Answer 1

Answer:

1) 1023

2) 8

Step-by-step explanation:

1)

Given:

$a_{n+1}=2\cdot a_n + 1$ and $a_1 = 1$

Then,  the next table can be computed (only the first terms are explicitely shown)

n      $a_n$

1       1

2      $a_{2}=2\cdot 1 + 1 =$ 3

3      $a_{3}=2\cdot 3 + 1 =$7

4      15

5      31

6      63

7      127

8      255

9      511

10     1023

2)

Given

$t_n=n^2-2n$

Then,  the next table can be computed

n      $t_n$

1       $t_1=1^2-2(1) =$-1

2      $t_2=2^2-2(2) =$0

3      $t_3=3^2-2(3) =$3

4      $t_4=4^2-2(4) =$8