Question

11. The sum of first n natural numbers is given nin=1
by the formula S = n*. If the sum of first x natural numbers is 66. find the value of x.​

Answer 1

Step-by-step explanation:

S=

2

n(n+1)

⇒231=

2

n(n+1)

⇒n

2

+n−462=0

⇒n

2

+22n−21n−462=0

⇒n(n+22)−21(n+22)=0

⇒(n+22)(n−21)=0

⇒n=−22 or n=21

∴n=21 as n=−22 is not a natural number.

Answer 2

Answer:

12

Step-by-step explanation:

Sum of first n consecutive natural numbers =

n(n+1)/2

So

x(x+1)/2 = 66

x(x+1) = 132

x² + x - 132 = 0

x² + 13x - 12x - 132 = 0

(x+13)(x-12) = 0

x = - 13 or 12

But All natural numbers > 0. So, - 13 is rejected.

12 is the answer