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

1) 1023

2) 8

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