Question

find the sum of the even number between 51 and 100​

Answer 1

Step-by-step explanation:

Natural numbers are similar to arithmetic progression, thus to find the sum from 51 to 100, we can use the formula = N(a+l)/2, where N is the total number of terms to be added. * Answer is 50(51+100)/2 = 3775.

Answer 2

Answer:

sum of the even number between $51$and $100$ is $1800.$

Step-by-step explanation:

Natural numbers are a part of the number system, including all the positive numbers from 1 to infinity. Natural numbers are also called counting numbers because they do not include zero or negative numbers.

Natural numbers are the numbers that are used for counting and are a part of real numbers. The set of natural numbers includes only the positive integers, i.e., $1, 2, 3, 4, 5, 6, ...........\infty$.

An even number is a number that is a multiple of 2.

$2,4,6,8............$

Arithmetic Progression (AP) is a sequence of numbers in order, in which the difference between any two consecutive numbers is a constant value. It is also called Arithmetic Sequence.

Given: Even number between 51 and 100​.

Find: the sum of the even number between 51 and 100​.

Sequence of Arithmetic Progression:

$52,54,56.....98$

First number, $a=52$

last number, $l=98$

difference,$d=2$

we know that

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

$98=52+(n-1)2\\2(n-1)=98-52\\2(n-1)=46\\n-1=23\\n=23+1\\n=24$

Total number between 51 and 100 is 24.

Sum of the even number between 51 and 100​ is:

$S_{n} =\frac{n}{2} (a+l)\\\\S_{n}=\frac{24}{2} (52+98)\\\\S_{n}=12(150)\\S_{n}=1800$

Hence, sum of the even number between 51 and 100​ is 1800.

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