Suppose, a_{1},a_{2},a_{3},………an are the terms of an A.P.

Then,a_{2} = a_{1}+d, a_{3} = a_{2}+d , where a_{1} is the 1st term & d is the common difference which is constant for an Arithmetic Progression

In general,a_{n+1} = a_{n+d} , where n is any natural number.

For example**,**

2, 5, 8, 11……… is an A.P with common difference 3.

3, 9, 15, 20…… is not an A.P because a_{4}–a_{3} = 5 which is not equal to (a_{2}–a_{1}).

5, 1, -3, -7……..is an Arithmetic Progression with a common difference -4.

- If a constant is added to or is subtracted from each term of an Arithmetic Progression, then the resulting sequence is also an Arithmetic Progression with the same common difference.
- Each term of an Arithmetic Progression is multiplied by a constant or divided by a "non-zero" constant then resulting sequence is also an Arithmetic Progression.

a_{1},a_{2},a_{3}……..a_{n} is an A.P,

It can be written as- a, a+ d, a + 2d, a + 3d … … a + (n – 1) d, where a is the first term, n is the number of terms and d is common difference.

nth term of an A.P : a_{n} = a+(n–1)d

Given, a_{11}=5, a_{5} = 11

a + 10d =5—–(1)

a + 4d= 1—–(2)

Subtract (2) from (1) from gives,

6d =−6

d= −1

Putting d = -1 in ——(1), a – 10 = 5

a= 10+5= 15

a_{16} = a+15d

a_{16} = 15+5(−1) =0

Must Read Arithmetic Progression Articles

- Arithmetic Progression: Concepts & Tricks
- Arithmetic Progression: Solved Examples

If number ‘c’ can be inserted between 2 numbers a and b such that a, c, b forms an Arithmetic Progression, then c is called the Arithmetic Mean of a and b

c–a = b–c

2c= a+b

c = (a+b)/2

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Let 10,M_{1},M_{2},M_{3},M_{4}, 25 be the resulting sequence.

Common difference, d = (25–10)/ (4+1) =15/5 = 3

M_{1} = 10+3= 13

M_{2} = 10+2*3 = 16

M_{3}= 10+3*3 = 19

M_{4} = 10+4*3 =22

10, 13, 16, 19, 22, 25 is an Arithmetic Progression with common difference 3.