Question

Consider the following 7 natural numbers: 6,8,11, 16, 19, 22, 23. a) Three of these numbers can be decomposed in the form 2. A + 1, where A is another natural number. Which three numbers can be written in this form? Show your work. b) In one sentence, identify what the numbers in part a) have in common.

I need help with this! Someone explain please​

Answer 1

a) The numbers that can be decomposed in the form 2A + 1 are the ones that are odd when subtracted by 1 and then divided by 2. So, we can check each number to see if it satisfies this condition:

6: (6 - 1)/2 = 2.5 (not a natural number)

8: (8 - 1)/2 = 3.5 (not a natural number)

11: (11 - 1)/2 = 5

16: (16 - 1)/2 = 7.5 (not a natural number)

19: (19 - 1)/2 = 9

22: (22 - 1)/2 = 10.5 (not a natural number)

23: (23 - 1)/2 = 11

So, the three numbers that can be decomposed in the form 2A + 1 are 11, 19, and 23.

b) The numbers in part a) have in common that they are odd.