Question

The sum of the first n natural number is 210.find the number

Answer 1

Step-by-step explanation:

First natural number is 1.

Sn=n/2[2a+(n-1)d]

210=n/2[2+(n-1)]

420=2n+n(n-1)

420=n^2+n

n^2+n-420=0

n^2+21n-20n-420=0

n(n+21)-20(n+21)=0

(n+21)(n-20)=0

n=-21 or 20

But n cant be negative

n=20

The natural numbers are

1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19 and 20 .

Answer 2

Answer:

Sum of n natural number =210

n(n+1)/2=210

n ki power 2

(n2+n)/2=210

n2+n= 210*2

n2+n=420

n2+n-420

n2+21n-20n-420=0

(n2+21n)-(20n+420)=0

n(n+21)-20(n+21)=0

(n-20) (n+2)=0

Ans