nth term of Arithmetic Progression at Algebra Den

Arithmetic

Additive Identity
Arithmetic Progression
Associative Property
Averages
Brackets
Closure Property
Commutative Property
Conversion of Measurement Units
Cube Root
Decimal
Distributivity of Multiplication over Addition
Divisibility Principles
Equality
Exponents
Factors
Fractions
Fundamental Operations
H.C.F / G.C.D
Integers
L.C.M
Multiples
Multiplicative Identity
Multiplicative Inverse
Numbers
Percentages
Profit and Loss
Ratio and Proportion
Simple Interest
Square Root
Unitary Method

Algebra

Cartesian System
Order Relation
Polynomials
Probability
Standard Identities & their applications
Transpose

Geometry

Basic Geometrical Terms
Circle
Curves
Angles
Define Line, Line Segment and Rays
Non-Collinear Points
Parallelogram
Rectangle
Rhombus
Square
Three dimensional object
Trapezium
Triangle
Quadrilateral

Trigonometry

Trigonometry Ratios

Data-Handling

Arithmetic Mean
Frequency Distribution Table
Graphs
Median
Mode
Range

Videos
Solved Problems

Home >> Arithmetic Progression >> nth Term >>

nth term of Arithmetic Progression

Arithmetic Progression : Common Difference nth Term

Formula to calculate nth Term of Arithmetic Progression (AP):

a_n = a + (n – 1) d

Let's understand this formula with the help of following examples:

Example 1: Find the 6th term of Arithmetic Progression (AP) 5, 7, 9 ...
Solution: In the given Arithmetic Progression (AP), we have:

1st Term i.e. a = 5
common difference i.e. d (difference between any term) = 7 - 5 = 2
n = 6 (given)

Now use formula to find nth term:
a_n = a + (n - 1) d

Put the values of a, d and n from above and we get:
a₆ = 5 + (6 - 1) 2

solve brackets and we get:
a₆ = 5 + (5) 2
a₆ = 5 + 10
a₆ = 15

Hence, the 6th term of Arithmetic Progression (AP) 5, 7, 9 ... is 15

Example 2: Find the 10th term of Arithmetic Progression (AP) 34, 31, 28, 25 ...
Solution: In the given Arithmetic Progression (AP), we have:

1st Term i.e. a = 31
common difference i.e. d (difference between any term) = 34 - 31 = -3
n = 10 (given)

Now use formula to find nth term:
a_n = a + (n - 1) d

Put the values of a, d and n from above and we get:
a¹⁰ = 34 + (10 - 1) -3

solve brackets and we get:
a₁₀ = 34 + (9) -3
a₁₀ = 34 -27
a₁₀ = 7

Hence, the 10th term of Arithmetic Progression (AP) 4, 31, 28, 25 ... is 7