Question

Consider the following process. Start with the numbers 1 and 4. A third number is created by taking the sum of the previous two numbers, which in this case gives us 5. Then, a fourth number is obtained by adding 4 and 5. This process can be repeated to create a sequence of numbers.

Answer 1

We get a sequence of numbers:

`S=\{1, 4, 5, 9, 14, 23, ...\}`

Explanation:

Start with the numbers 1 and 4. A third number is created by taking the sum of the previous two numbers, which in this case gives us 5. Then, a fourth number is obtained by adding 4 and 5.

We have:

`a_1=1\\\\a_2=4\\\\a_3=a_1+a_2=5\\\\a_4=a_3+a_2=9\\\\a_5=a_4+a_3=14\\\\a_6=a_5+a_4=23\\\\a_7=...`

We get a sequence of numbers:

`S=\{1, 4, 5, 9, 14, 23, ...\}`.

Answer 2

The solution is in the attachment