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Ankit patter

the sum S of first n even natural number is given by the relation S=n(n+1).find n if the sum is 420

Posted in Algebra, asked by Ankit patter, 6 years ago. 11815 hits.

25

420=n(n+1) solve bracket
420=n+ n take 420 to the other side 
n2 + n - 420 = 0 apply quadritic form

n2  - 20n+ 21n - 420 = 0 now factorize it 
n(n-20) +21(n-20)=0
(n-20)(n+21)=0

n-20=0 , n+21=0
n=20 , n=-21


no of terms can never b negative, so the answer is 20

mariam khan
mariam khan - 6 years ago
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24

420 = n (n + 1 )      use distributive property

400 + 20 = n+ n     transpose

400 - n= n - 20     get the square root of 400 - nthen it becomes

20 - n = n - 20        transpose

20 + 20 = n + n       then add

40 = 2n         then divide by 2 on each side to get the value of n

n = 20

 

 


 

Reynan Flores
Reynan Flores - 6 years ago
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6

Sum of first n even natural numbers  is S=n(n-1)

Given Sum = 420

so, n(n-1) = 420

n^2-n=420

n^2-n-420=0

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

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

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

n=20 or n=-21

But here n is the number of first n natural numbers so n cannot be negative. so n=20

vinu omanan
vinu omanan - 6 years ago
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2

given the sum of n even numbers n(n+1)=420

                                                =n^2+n=420

                                                 =n^2+n-420---(1)

now we have to do factorization,so we have multiply the first term of and constant from equation(1) . then  we will get, -420n^2

 now we have divide the value into tow values .when we add or substarct the 420n^2 we have to get the middle term of the equation and also when we multiply it we have to get again -420n^2

so  now we have to do, -420n^2= 21n*-20n

now we will rewrite the eqn(1),

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

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

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

                                                    =n+21=0,n-20=0

                                                   =n=-21,n=20

given problem is,the sum of even number so we will  take n=20  only

  so,n(n+1)=>20(20+1)=>20(21)=>420

Venkat Nagendra Thati
Venkat Nagendra Thati - 6 years ago
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