Question

if the mean of 1,2,3,...,x is 6x÷11,find the value of x

Answer 1

Answer:

Terms: 1, 2, 3, .... x

Sum of n terms of an AP is given by the expression: $\dfrac{n ( n + 1 )}{2}$

In this case it would be, $\dfrac{x ( x + 1 )}{2}$

Mean = Sum of terms / Number of terms

Also given that, mean = 6x / 11

Hence substituting the values we get,

$\dfrac{6x}{11}  = \dfrac{ x(x+1)}{2} \times \dfrac{1}{x} \\\\\implies \dfrac{6x}{11} = \dfrac{x(x+1)}{2x} \\\\\text{Cross multiplying the terms we get,} \\\\\implies 6x \times 2x = 11 ( x ( x + 1 ) \\\\\implies 12x^2 = 11 ( x^2 + x ) \\\\\implies 12x^2 = 11x^2 + 11x \\\\\implies 12x^2 - 11x^2 = 11x \\\\\implies x^2 = 11x \\\\\implies x = 11$

Hence the value of x is 11.

Answer 2

Thank you for asking this question. Here is your answer:

First of all we will find the mean.

Mean  = Sum/no.

6x/11=[x/2(1+x)]÷x

6x^2/11=(x+x^2)÷2

12x^2/11=x+x^2

12x^2=11x+11x^2

x^2=11x

x^2/x=11

x=11

11 is the final answer.

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