A. P. conceptual Notes

➥ Arithmetic progression is a series of numbers with same common difference between each two consecutive numbers.

General Representation
a₁, a₂, a₃, a₄,...

General form of an AP
a , a+d , a+2d , a+3d , a+4d ,...
where a = first term and d = Common difference
we can also write
First term (a₁) = a
Second term (a₂) = a+2d
Third term (a₃) =a+3d and so on...

How to FInD common difference

Formula
d = a_(n+1) — a_n

d_(n+1) = d_n
∴ A. P. exist

d_(n+1) ≠ d_n
∴ A. P. does not exist.

where n is an integer.
d = common difference

➤If common difference (d) between each two consecutive numbers not same, then series isn't A.P.

Find n^th term:-

QA:- A.P.- 2, 5, 8,...

FORMULA
a_n = a+(n-1)d

where, a_n -n^th term
a - first term
n - no. of term
d - common difference

AP 2, 5, 8,...

Suppose we have to find 6th term of above given series.

First term of A.P. is (a) = 2
finding 6th term
∴ n = 6
common difference (d) = 3

Ans. By using above formula,
a₆ = 2+(6-1)3
= 2+5x3
= 17

You can fiND below Qus. by the above series.

1. Find 9^th term
2. Find 23^th term
3. find 37^th term
4. Find 43^th term

Answer

A.1: 26
A.2: 68
A.3: 110
A.4: 128

PRACTICE

QB:-A.P.- 4, 9, 14,...

1. Find 11^th
2. Find 22^th
3. Find 35^th
4. Find 77^th

Answer

B.1: 54
B.2: 109
B.3: 174
B.4: 384

Find n^th term of an A.P. from the end

FORMULA
T_(m-n+1) = a+(m-n)d

A.P. having m terms
a = First term
d = common difference
n = nth term from the end

QC:- A.P.- 1, 3, 5, ?, 9, 11
Find 3rd term from the end by the above formula.

First term (a) = 1
n = 3
m = 6
common difference (d) = 2

Put all these values in above formula...
T₄ = 1 + (6-3)2
= 1 + 3x2
= 7 Ans.

QD:- A.P.- 2, 5, 8,...101
Find 9th term from the end.

Answer

77