Question

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

Answer 1

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!!! :)

Answer 2

Answer:

when a= 2 d =2 then sum = n(n+1)

Step-by-step explanation:

sumis 420

$420 = n(n + 1) \\ 420 = n {}^{2} + n \\n {}^{2} + n - 420 = 0\\ n {}^{2} + 21n - 20n - 420 = 0 \\ n(n + 21) - 20(n + 21) = 0 \\( n + 21)(n + - 20) = 0 \\ n = 20\: \: \: \:n = - 21 \\ n = 20 \: because \: n \: cant \: be \: negative$

n(n+1)