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.
(class 10 CBSE SAMPLE PAPER 2017-18 MATHS)
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54
SOLUTION:
GIVEN:
Sum(Sn)= 420
Sn= n(n+1)
420= n²+n
n²+n -420=0
n²+21n-20n-420= 0
(By middle term splitting)
n(n+21) - 20(n+21)=0
(n+21)(n-20)=0
n+21=0
n= - 21
n-20= 0
n= 20
n= -21, 20
( n cannot be negative)
Hence, n = 20
Hope this will help you….
GIVEN:
Sum(Sn)= 420
Sn= n(n+1)
420= n²+n
n²+n -420=0
n²+21n-20n-420= 0
(By middle term splitting)
n(n+21) - 20(n+21)=0
(n+21)(n-20)=0
n+21=0
n= - 21
n-20= 0
n= 20
n= -21, 20
( n cannot be negative)
Hence, n = 20
Hope this will help you….
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