Question

Arithmetic progression explain

Answer 1

Visual proof of the derivation of arithmetic progression formulas – the faded blocks are a rotated copy of the arithmetic progression
In mathematics, an arithmetic progression (AP) or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant. For instance, the sequence 5, 7, 9, 11, 13, 15, . . . is an arithmetic progression with common difference of 2.

If the initial term of an arithmetic progression is {\displaystyle a_{1}} and the common difference of successive members is d, then the nth term of the sequence ( {\displaystyle a_{n}}) is given by:

{\displaystyle \ a_{n}=a_{1}+(n-1)d},
and in general

{\displaystyle \ a_{n}=a_{m}+(n-m)d}.
A finite portion of an arithmetic progression is called a finite arithmetic progression and sometimes just called an arithmetic progression. The sum of a finite arithmetic progression is called an arithmetic series.

Answer 2

$\textbf{Answer :}$




$\huge\textbf{Arithmetic progression :}$




It is a sequence of numbers in which the different between two consecutive terms is constant.

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$\huge\textbf{Example :}$




a, a + d, a + 2d, a + 3d ....... (and so on).




→ 2, 4, 6, 8, 10....

In this d = 2

2, 2 + 2, 2 + 2(2), 2 + 3(2), 2 + 4(2)....

2, 4, 2 + 6, 2 + 8....

So, the arithmetic progression came is 

2, 4, 6, 8, 10....




→ 4, 8, 12, 16, 20.....

In this d = 4



→ 9, 18, 27, 36, 45, 54 ....

In this d = 9


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