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Hey learners,

hope you are doing well.##

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hope you are doing well.

Today I’m here with ** Arithmetic progression** topic, for this topic I can say it has given an access to hidden treasure of Mathematics .

So, __I’m starting with general intro with some basics of arithmetic progression .__

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What is Arithmetic progression (AP) /Arithmetic Sequence

__Definition:__

progression are refers to series formations,

and those series formations in which the terms are lying at same gaps are called as Arithmetic progression or AP.

further more I can state that in this series the difference between two consecutive terms remain same Examples:

2, 4, 6, 8……

1, 3, 5, 7……

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- How long the series can be ?

This doesn’t have any criteria or any boundation, means the number of terms of series can be infinite, unless number of terms given in the question.

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- What Significance arithmetic series has ?

A number of significance this topic contains among those some are, (

*with proper values and formula we can evaluate*)####
* We can identify the number of terms of any series*
** We can identify the missing terms.**
** We can identify the value of last terms.**
**We can find the sum of all the terms of given series**

*We can identify the number of terms of any series***We can identify the missing terms.****We can identify the value of last terms.****We can find the sum of all the terms of given series**
let we are having any series

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**5, 10, 15, 20, 25, 30…….up to 35th term**
now it is being crucial to add one after one to find the sum of all the terms like

5 + 10 + 15 +20 +…….up to 35th term.

(nobody wants to do this for each problem)

to overcome from this, AP and its applications are derived.

**• similarly we can also evaluate 35th term directly.**

**• I think I’ve given complete clarification regarding Arithmetic progression and it’s existence.**

**• In this post I’m revealing the Formula of AP only, further discussion on topic will be carry forwarded to our next posts.****Formula of AP:**

**T = A + (n-1)D**

**where,**

**T – last term, nth term of series.**

**A – first term of series.**

**n – number of terms.**

**D – common difference between to consecutive terms.**

so,

If you still have some doubts, let me know in comment section, I’ll be pleased to hear from you.

Stay tuned for the same topic for formula and Q/SOL. and many more…

see you in next post.

Thanks.