Find the sum integers from 8 and 35

Find the sum integers from 8 and 35

Answer :

Determine the sum of the integers from 8 and 35

Before discussing the problem, let us first know what is an integer? What is the definition of integer? What is the definition of an integer?

Integers are a collection of numbers whose shape is round. And integers are not decimal numbers, nor are they fractional numbers, but they can also be called full numbers. Integers are divided into 3, namely positive numbers, negative numbers, and neutral numbers, namely 0. Usually integers can be represented by a number line.

From the above definition, it can be understood that integers are a combination of the set of whole numbers and negative numbers, or a combination of natural numbers, 0, and negative numbers.

Integers are denoted by Z which comes from the word ZAHLEN (German) which means number.

After understanding the definition, let’s discuss the problem: The sum of the integers from 8 and 35.

Is known:

a=8

?f=a %7Bn%7D=35

b=1

n=35-7=28

?f=a %7Bn%7D%3Da%2B(n 1)b

?f=S %7Bn%7D%3D%5Cfrac%7Bn%7D%7B2%7D(2a%2B(n 1)b)

Asked:

?f=S %7B28%7D=…

Answer:

?f=S %7Bn%7D%3D%5Cfrac%7Bn%7D%7B2%7D(2a%2B(n 1)b)

?f=S %7B28%7D%3D%5Cfrac%7B28%7D%7B2%7D(2(8)%2B(28 1)1)

?f=S %7B28%7D%3D%5Cfrac%7B28%7D%7B2%7D(16%2B27)

?f=S %7B28%7D%3D%5Cfrac%7B28%7D%7B2%7D(43)

?f=S %7B28%7D%3D(14)(43)

?f=S %7B28%7D%3D602

It turns out that the sum of the integers from 8 to 35 is 602. Let’s look for it manually.

8+9+10+11+12+13+14+15+16+17+18+19+20+21+22+23+24+25+26+27+28+29+30+31+32+ 33+34+35=…

35+8=43

34+9=43

33+10=43

………….

21+22=43

So the sum of these integers is 43×14=602.

Please note there is a question difference between:

1. Find the sum of the integers from 8 and 35

2. Find the sum of the integers between 8 and 35.

For the first question, the answer is like the answer above, while for the second question the numbers 8 and 35 are not counted. Why? Because the numbers between 8 and 35 are 9,10,11,12,…,33,34,35. So it is very important to pay attention to the language. Therefore it is necessary to be careful to understand the problem.

 

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