Question

Write The Sum Of All Even Integers Between 99 And 301

Answer 1

Answer:

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 ? From here, we'll evaluate the sum 50+51+52+... +149+150, and then double it

Step-by-step explanation:

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Answer 2

Solution:

First even integer between 99 & 301 is 100 and last even integer between them is 300.

It will form the following series

100, 102, 104,..........,300

Here, we have

first term (a) = 100

common difference (d)

= second term - first term

= 102 - 100

= 2

last term (an or l) = 300

We will find n (number of terms) by the formula

an ( l) = a + (n-1)d

=> 300 = 100 + (n-1)2

=> 200 = (n-1)2

=> 200/2 = n-1

=> 100 = n-1

=> n = 101

Sum of n terms of an Arithmetic progression is given by, Sn

Sn = n/2 [2a+(n-1)d]

S101 = 101/2 [2×100+ (101-1)2]

S101 = 101/2 [200 + 100×2]

S101 = 101/2 [200 + 200]

S101 = 101/2 (400)

S101 = 101 × 200

S101 = 20200

We can also find sum of n terms by this formula,

Sn = n/2 [a+l] (derived from previous formula)

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

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