For any positive integer n, the sum of the first n positive integers equals n ( n 1 ) 2 . What is the sum of all the even integers between 99 and 301

The sum of all the even integers between 99 and 301 is 20200

Step-by-step explanation:

For the sum of all the even integers between 99 and 301, this can be calculated using the formula for Sum of n terms in an Arithmetic Progression (AP)

Sum of n terms in an AP =

Where is the number of terms

is the first term

and is the common difference

The AP for the sum of all the even integers between 99 and 301 will look like

100 + 102 + 104 + ... + 300

= 100

can be calculated by taking the difference of the first two terms or any two consecutive terms of the AP

Hence, = 102 - 100 = 2

can be determined from the formula used to calculate the Last term of an AP

Where is the last term

In the AP, the last term, = 300

Then

Hence, there are 101 terms in the AP

Now, to determine the sum

=

Hence, the sum of all the even integers between 99 and 301 is 20200

dilation scale factor 2: starting with δabc, draw the dilation image of the triangle with a center at the origin and a scale factor of two. notice that every coordinate of the original triangle has been multiplied by the scale factor (x2). dilation with scale factor 2, multiply by 2.