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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