Question

# Use inductive reasoning to make a conjecture about the sum of a number and itself. Then use deductive reasoning to show the conjecture is true.

Hint:

### Inductive Reasoning is the process of drawing a general conclusion by observing a pattern based on the observations and this conclusion is called conjecture.

Deductive reasoning is the process by which a person makes conclusions based on previously known facts.

## The correct answer is: Hence, we conclude that the result is the number multiplied by 2 and we have proved this conjecture by deductive reasoning.

### Let’s create a conjecture for the numbers -1, 4, 9, 65, and 200. We are asked to make a conjecture about the sum of a number and itself.

So first, do the sum of numbers with itself. We got

-1 + (-1) = -2

4 + 4 = 8

9 + 9 = 18

65 + 65 = 130

200 + 200 = 400

the conjecture is true or not by deductive reasoning. Let’s say the number is x. Adding the number by itself.

x + x = 2x

So, we can see that the result is the number multiplied by 2 so our conjecture is true.

Final Answer:

Hence, we conclude that the result is the number multiplied by 2 and we have proved this conjecture by deductive reasoning.

Informally, a hypothesis is just drawing assumptions about something based on what you already know and have observed.

A conjecture is formally defined as a based-on-observations, a statement considered true.

Speculation is similar to your opinion about something you follow or perhaps a knowledgeable estimate.

For example, observe the numbers below: 2, 4, 6, 8, 10, and 12. What number would come next? You're probably thinking 14, but What led you to that conclusion, and why? You may have seen the pattern and that the list is counting in twos.

The following number is 14 because the list counts by 2's, according to your hypothesis.

You saw the pattern and concluded without making any claim.