In an arithmetic progression (AP), the differences between every two consecutive terms are all same whereas in a geometric progression (GP), the ratios of every two consecutive terms are all same.

What is the Difference Between Arithmetic and Geometric Progressions? Here, a n represents the n th term and S n represents the sum of the first n terms. Here are the formulas of different types of progressions. There are three types of progressions: AP (Arithmetic Progression), GP (Geometric Progression), and HP (Harmonic Progression). is a progression as there is a pattern where each number is obtained by multiplying its previous number by 1/2 and each number can be written as (1/2) n (where 'n' represents the term's ordinal number). Progression is a sequence of numbers that show a pattern. The reciprocal of terms in harmonic progression form an arithmetic progression.įAQs on Progression What is the Meaning of a Progression?.In a geometric progression, each successive term is obtained by multiplying the common ratio to its preceding term.In an arithmetic progression, each successive term is obtained by adding the common difference to its preceding term.Sum of the first n terms, S n = 1/d ln / (2a - d) ].Reciprocal of the sequence: 2, 4, 6, 8.This sequence is a harmonic progression because the reciprocal of all the terms of this progression form an arithmetic progression. Now the sequence of heights formed by the ball is: 1/2, 1/4, 1/6, 1/8. After the third impact, the height attained by the ball is 1/8 units, and so on. After the second impact, the height attained by the ball is 1/6 units. When a ball is dropped, the initial height reached by the ball is 1/2 units and after the first impact, the height attained by the ball is 1/4 units. So, taking reciprocals of each term we get 1,1/2,1/3,1/4. The sequence of natural numbers is an arithmetic progression. Sum of infinite geometric series, S ∞ = a / (1 - r) when |r| Sum of the first 'n' terms, Sₙ = a(r n - 1) / (r - 1) when r ≠ 1 and Sₙ = na when r = 1.Then, the geometric progression formulas are given by: Let the first term of the progression be a, the common ratio be r, and the n th term be a n. In general, a geometric progression looks like this:Ĭonsider an example of a geometric progression: 1, 4, 16, 64. is a GP as every number is obtained by multiplying a fixed number 4 to its previous term. This fixed number is called the common ratio. Sum of the first n terms, S n = n/2(2a+(n-1)d) (or) S n = n/2(a + l), where l = the last term = T n.Ī geometric progression (GP) is a sequence of numbers in which each successive term is the product of its preceding term and a fixed number.

Then, the arithmetic progression formulas are given by: Let the first term of the progression be a, the common difference be d, and the n th term be a n. This fixed number is called the common difference (It can be positive, negative, or zero). The succeeding terms are obtained by adding a fixed number, that is, $3. So, the amount in her piggy bank follows the pattern of $30, $33, $36, and so on. She increased the amount she put in her piggy bank on each successive birthday by $3.

'd' is the common difference (fixed number)įor example, Minnie put $30 in her piggy bank when she was 7 years old.

In general, an arithmetic progression looks like this: is an AP as every number is obtained by adding a fixed number 3 to its previous term. This fixed number is called the common difference. An arithmetic progression (AP) is a sequence of numbers in which each successive term is the sum of its preceding term and a fixed number.

Type of sequence and examples