If the sum of the even integers between 1 and k, inclusive, is equal to 2k, what is the value of k?

K = 6

Step-by-step explanation:

Even integers between 1 and k will be 2, 4, 6, 8, 10.........(k-2), k

Therefore, number of even terms between 1 and k inclusive will be

Now we know these even integers will form an arithmetic sequence which has it's first term as 2 and a common difference of 2.

We know sum of an arithmetic sequence is represented by

=

where a = first term

n = number of therms

d = common difference

2k =

2k =

2k =

8k = k[k + 2]

8 = k + 2

k = 8 - 2

k = 6

a. the are of the rectangle is 18.25

b. 18.25 times two is 36.50

rae me : d