ARITHMETIC PROGRESSION

ARITHMETIC PROGRESSION

Sequence – The arrangement of the numbers according to some rule.

Examples

1) 2, 4, 6, 8, 10, .......

2) 10, 20, 40, 80, .....

3) 1, 4, 9, 16, 25,.......

4) 6, 4, 2, 0, -2, -4,.......

Arithmetic Progression – The sequence in which the difference between any two consecutive numbers is constant.

Examples

1) 10, 20, 30, 40,.....

2) 15, 10, 5, 0, -5,......

The difference between the numbers is called as “Common Difference”.

The common difference is denoted by ‘d’.

The first term is denoted by ‘a’

The c.d. can be zero, positive or negative.

The succeeding number is AP is obtained by adding c.d. to the preceding number.

A.P. à 10, 13, 16, 19,........

Here, first term, a = 10                      d = 13 – 10 = 3

For 16,

Preceding term à 16 – 3 = 13

Succeeding term à 16 + 3 = 19

If AP, a₁, a₂, a₃, a₄, a₅, .............a_n

n^th term of an AP à a_n = a + (n-1)d

a_n – n^th term of an AP                        a – first term of an AP

d – c.d.                                              n – number of terms

Same formula can be used to find ‘a’, ‘n’ or ‘d’

Sum of the n term of an AP (Sn)

S_n = n/2[2a + (n-1)d]               S_n = n/2(a + l)      l – last term of AP


Check the link for the explanation of AP - https://youtu.be/eczjDmDgw-o