Question

2+4+6+8+.....+2k=90 then the value of k

Answer 1

We are given, 2+4+6+..............+2k = 90

clearly, a = 2

and,    d = 2

Let there are n terms,

so, an = 2k

2 + (n-1)2 = 2k

so, 2n = 2k

Hence, n = k  ------------------------------------------------(1)

We are also given, sn  = 90

so, n(a+2k)/2 = 90

=> k(2+2k)/2 = 90                                 [Using (1) n = k]

k(k+1) = 90

so, k^2 + k - 90 = 0

Hence, k = -10 or k = 9

k can't be negative

Thus, Answer is k = 9

Answer 2

Answer: 9

Step-by-step explanation:

2+4+6+8+.....+2k=90

2(1+2+......+k) = 90

2]k(k+1)/2] =90

k² + k - 45 =90

(k+10)(k-9)=0

k=9 0r k= -10

k can only be 9 as it is a count and can't be negative