6) If the sun
of first n even
natural
number is 420, then
value of n
is
Answers
Answer:
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Step-by-step explanation:
∴n=20. So, this is your answer. Note: We can also solve these types of problems by using the concept of arithmetic progression as the sum is given, the first term and common difference can be determined and the number of terms n is found. In this case Sn=420, a=2 and d=2.
Answer:
n = 20
Step-by-step explanation:
since it's natural even number it will start from 2
In A.P.,
2+4+6+8+....+n = 420
First Term (a) = 2
Common Difference (d) = 4-2 = 2
nth term (tn) = a + (n-1)d
=> tn = 2 + (n-1)2
=> tn = 2 + 2n-2
=> tn = 2n
Sum (S) = (n/2) (a+tn)
=> 420 = (n/2) (2 + 2n)
=> 840 = n( 2n+2)
=> 840 = 2n²+2n
=> 2n²+2n-840=0
=> n²+n-420=0
=> n²+21n-20n-420=0
=> n(n+21)-20(n+21)=0
=> (n-20)(n+21) = 0
=> n = 20 or -21
but term can never be negative, so n=20