1.

The sum of some even numbers is starting from 2 is 420.find the number of even numbers added?​

Answer»

AP: 2, 4, 6..........

a=2, d=2, Sum=420, n=?

We know,

Sum= n/2 {2a + (n-1)d}

420= n/2 {2(2) + (n-1)2}

420= n/2 {4+2n-2}

420= n (2n+2)

2

420= n × 2(n+1)

2

420= n(n+1)

420= n²+n

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

n cannot be negative

Hence n=20.

Hope it helps!!! :)


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