Question

the sum of the first n consecutive even be found using S = n² + n where n > 2 what is the value of n when the sum is 30A) 5B) -6C) -5D)6

Answer 1

Given:

a.) The sum of the first n consecutive even be found using S = n² + n where n > 2.

Let's determine the value of n at S = 30.

`\text{ S = n}^2\text{ + n}`
`\text{ 30 = n}^2\text{ + n}`
`\text{ n}^2\text{ + n - 30 = 0}`

Where, a = 1, b = 1 and c = -30

Using the quadratic formula:

`\text{ n = x =}\frac{-\text{b }\pm\text{ }\sqrt[]{b^2\text{ - 4ac}}}{\text{ 2a}}\text{ = }\frac{\text{ -1 }\pm\text{ }\sqrt[]{(1)^2-4(1)(-30)}}{\text{ 2(1)}}`
`\text{ = }\frac{\text{ -1 }\pm\text{ }\sqrt[]{1\text{ + 120}}}{2}\text{ = }\frac{\text{ -1 }\pm\text{ }\sqrt[]{121}}{2}`
`\text{ n = }\frac{\text{ -1 }\pm\text{ 11}}{\text{ 2}}`
`\text{ n}_1\text{ = }\frac{-1\text{ + 11}}{2}\text{ = }(10)/(2)\text{ = 5}`
`\text{ n}_2\text{ = }\frac{-1\text{ - 11}}{\text{ 2}}\text{ = }\frac{\text{ -12}}{\text{ 2}}\text{ = -6}`

Therefore, there are two possible values of n, it is 5 and -6.

The answer is letter A and B.