Maths-
General
Easy

Question

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

hintHint:

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 =fraction numerator n left parenthesis n plus 1 right parenthesis over denominator 2 end fraction.
    The sum of numbers from 1 to 7 = fraction numerator n left parenthesis n plus 1 right parenthesis over denominator 2 end fraction  =  fraction numerator 7 left parenthesis 7 plus 1 right parenthesis over denominator 2 end fraction = 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 fraction numerator n left parenthesis n plus 1 right parenthesis over denominator 2 end fraction.

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