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Arithmetic progression-all you need to know!

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Arithmetic progression-all you need to know!

When the difference between the consecutive terms is constant mathematics we call it arithmetic sequence or arithmetic progression in the field of mathematics. 

This is not only bound to science and one can also observe this progression in his or her daily life. Like if you are at a bus stop and traffic is moving at a constant speed then you know when the next bus will arrive? The same is the case if you ride a taxi. At first, you will be charged an initial rate and then a per kilometer charge starts. So, we have thousands of examples in our daily routine regarding this topic. We just have to look around and observe hard. A mathematics boring topic always becomes more interesting if you find its daily usage. Math is fun!

Formula

Let’s take a look at how to calculate the arithmetic sequence:

If the difference is termed as d, the first term in the sequence is a1 then the nth term of the sequence will be:

Sn=n/2(a1+an)

Example:

Find 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 is 100. 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 submit the assignment the next day. Online arithmetic sequence calculators will do your job in just a few minutes. Try them out.

Arithmetic progression-all you need to know!

 

What is a midpoint?

When a middle line is divided into two equal segments starting from the center it is known as the midpoint. Distance is equal to both the endpoints. The segment is bisected with this midpoint. In elementary school training, these both are considered instrumental concepts. It is usually applied in the cartesian system and is a very common term.

Notation

M is used for the midpoint

Formula:

(a+c)/2,(b+d)/2

It is one of the simplest formulae and has been in use for a long time.

Arithmetic progression-all you need to know!

How to find midpoint in geometry?

The midpoint of a Line Segment

  1. Add both “x” coordinates, divide them by 2.
  2. Add both “y” coordinates, 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 by using just a graph and the answer seems like yes. But one should always keep this fact in mind while solving a problem. The graph or picture only suggests the answer and makes its picture. Only algebra will tell you the exact answer. So e.g if I have been provided with a problem of a midpoint and need to find it, I will first apply the midpoint formula.

After solving it, I will 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 which is indicated by the graph picture. On the other hand, when I performed all the calculations it was proven by algebra that it’s not exactly a bisector. So, our answer will be no, it’s not a bisector.

 

How to round-off the number?

It includes two basic steps and it’s very easy. We divide the numbers from 1-9 in two groups. One is from 1-4 and the other one is from 5-9. If a number falls in the Ist first group of 1-4 then an increasing number is added in it. When the number comes in a second range a 0 is automatically added. let’s take a look at one of the example:

  1. If you have a number like 0.977 then 7 falls in 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 the manual calculations are not doing the right thing then it is good to use a rounding calculator for quick results.

 

What are the rules for significance and significant figures?

Every problem comes with a solution and scientists from all over the world have come up with some common significance rules. Following rules are developed for determining whether the number is significant or not:

  1. If the number across zero contains a number less than 1 it is considered as a non-significant number e.g 000.097
  2. Zero is considered significant when it comes between two considerable numbers. E.g 2. 09 has three significant numbers.
  3. Whenever a zero comes after a decimal number or figure it is considered as significant. Eg. 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 as significant e.g 2.307

 

Using different unit complexity is avoided using these significant rules along with scientific notation problems. If you still have a problem then the online significant calculator is present to help you out. I hope this article has helped you clear your doubts regarding the significant numbers.

I am a researcher and a technical content writer. I love travelling, Love to explore new places, people & traditions. Football is more than a sport, Real Madrid forever. Madridista.

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