Maths-

General

Easy

Question

# Make a conjecture about the sum of numbers from 1 to 7. Write a conjecture for the general case.

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, the sum of numbers from 1 to n is (n(n+1))/2.

### Let’s first make a table and then look for the pattern

The sequence of the sum of numbers is 3, 6,10, 15, 21…..

We can see that

6 = 3 + 3

10 = 6 + 4

15 = 10 + 5

21 = 15 + 6

So by seeing the pattern, we can conclude a formula for the pattern for the sum of number from 1 to n =.

The sum of numbers from 1 to 7 = = = 28

And if we add numbers from 1 to 7 i.e. 1+2+3+4+5+6+7 is equal to 28. Hence, the conjecture is true

Final Answer:

Hence, the sum of numbers from 1 to n is .

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