Question

If the sum of first 'n' successive even natural numbers is 72, then formulate the quadratic equation to find n

Answer 1

Step-by-step explanation:

Formula for Sn for successive natural number = Sn = n(n+1)

2

72 = n(n+1)

2

144 = n2 + n

n2 + n - 144 = 0

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Answer 2

The quadratic equation is $n^{2}+n-72=0$

Explanation:

Given that the sum of first 'n' successive even natural numbers is 72.

The first 'n' even natural numbers are 2,4,6,8,10,.......

Thus, from the sequence $a=2$ and $d=2$

The sequence is an arithmetic sequence.

Thus, the sum of the sequence of the AP can be determined using the formula,

$S_n=\frac{n}{2} [2a+(n-1)d]$

Substituting $a=2$, $S_n=72$ and $d=2$ , we get,

$72=\frac{n}{2} [2(2)+(n-1)2]$

Simplifying, we have,

$72=\frac{n}{2} [4+2n-2]$

$72=\frac{n}{2} [2+2n]$

Multiplying the terms within the bracket, we have,

$72=n+n^2$

Subtracting both sides by 72, we have,

$n^{2}+n-72=0$

Thus, the quadratic equation is $n^{2}+n-72=0$

Learn more:

(1) If the sum of first n' successive even natural numbers is 72 then formulate the quadratic equation to find 'n'.

brainly.in/question/15424044

(2) The Sum Sn of first ‘n' even natural numbers is given by the relation Sn=n(n+1).Find n,if the sum is 420.

brainly.in/question/2006520