Question

Find positive integer x, if 1+2+3 +...+x=120.

Answer 1

Answer:

x = 15

Step-by-step explanation:

1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 +13 + 14 + 15 = 120

The number x is a positive integer.

Answer 2

Value of positive integer $x$ is equals to $15$.

What is integers?

" Integers is defined as collection of whole numbers and negative numbers."

Formula used

Sum of first $'n'$ natural numbers

$S_{n} = \frac{n(n + 1)}{2}$

According to the question,

Given positive integers,

$1 + 2 + 3 + ......... + x =120$

Substitute the value in the formula to get sum of positive integers,

$\frac{x(x+ 1)}{2}=120\\\\\implies x^{2} +x =240\\\\\implies x^{2} + x-240 =0\\\\\implies x^{2} +16x-15x -240=0\\\\\implies x (x+16) -15 (x+16) =0\\\\\implies (x+ 16) (x-15) =0\\\\\implies x = -16 or x =15$

$'x'$ is a positive integer. $x=-16$ is not possible.

Hence, Value of positive integer $x$ is equals to $15$.

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