andymartin

@andymartin · 15 Mar 2020

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Arithmetic progression - everything you need to know!

When the difference between consecutive terms is constant math, we call it sequence arithmetic or progression arithmetic in the field of mathematics.
This is not only linked to science, but you can also observe this progression in your daily life. For example, if you are at a bus stop and traffic is moving at a steady speed, do you know when the next bus will arrive? Maybe it's the case if you're traveling by taxi. At first you will be charged an initial fee and then a per-kilometer fee will be started. So, we have thousands of examples in our daily routine regarding this issue. We just have to look around and observe a lot. A boring topic of mathematics always becomes more interesting if it finds its daily use. Mathematics is fun!
Formula
Let's look at how to calculate the arithmetic sequence:
If the difference is called d, the first term of the sequence is a1 and then the nth term of the sequence will be:
Sn = n/2 (a1 + an)
Example:
Find the sum of the following arithmetic sequence 1,2,3... .99,100
So we have a total of 100 values, which means n = 100. The first value in this case is 1 and the last value is 100. The following values are added in the formula:
S100 = 100/2 (1 + 100) = 5050
Sometimes it's not easy to do all these long calculations by hand when you have to send the task the next day. The arithmetic sequence calculator online will do their job in just a few minutes. Try them.

How to find the midpoint in geometry?
The midpoint of a line segment
1. Add both “x” coordinates, divide them by 2.
2. Add both coordinates “y”, divide by 2 ·
Is y = 2x - 4.9 a bisector of the line segment with endpoints at (—1.8, 3.9) and
(8.2, —1.1)?
I can solve this using only one graph and the answer seems yes. But this fact should always be taken into account when solving a problem. The graph or image only suggests the answer and makes your image. Only algebra will tell you the exact answer. So, for example, if I have been given a problem of a midpoint and I need to find it, I will first apply the midpoint formula.

After solving it, will I tell you if this point is on the line or not?
y = 2x - 4.9
y = 2 (3.2) - 4.9 = 6.4 - 4.9 = 1.5
In this case, I want y = 1.4 but this is a bisector that is indicated in the graphic image. On the other hand, when I performed all the calculations, algebra proved that it is not exactly a bisector. So, our answer will be no, it's not a bisector.
How to round the number?
It includes two basic steps and is very easy. We divide the numbers from 1 to 9 into two groups. One is 1-4 and the other is 5-9. If a number falls into the first group of 1-4, then an increasing number is added. When the number comes in a second range, a 0 is automatically added. Let's take a look at one of the examples:
1. If you have a number like 0.977, then 7 falls into the second group, so it will be 0.90.
2. In the case of 2.33, it will be 2.4.
I hope you find these two basic rules very interesting, as I always find them very interesting. If manual calculations are not doing the right thing, then it's good to use a Rounding Calculator for quick results.

What are the rules of significance and significant figures?
Each problem comes with a solution and scientists around the world have created some common rules of importance. The following rules are developed to determine whether the number is significant or not:
1. If the number through zero contains a number less than 1, it is considered as a non-significant number, for example 000.097
2. Zero is considered significant when it comes to two significant numbers. For example, 2. 09 has three significant numbers.
3. Whenever a zero comes after a decimal number or figure, it is considered significant. E.g. 0.340 has four significant figures.
4. Exponential digits are not considered significant, e.g. 1.45 X10 ^ 6
5. Non-zero digits are considered significant, for example, 2,307
The use of different units of complexity is avoided by using these significant rules along with scientific notation problems. If you still have a problem, the meaningful online calculator is present to help you. I hope this article has helped you clarify your doubts about significant numbers. #arithmetic #arithmeticsequence #rounding #chemistry #calculus #algebra