Formulas related to progressions

Thread starter neenuroy
Start date Jul 16, 2004
Tags

Formulas

In summary, progressions are sequences of numbers that follow specific patterns or rules. There are different types of progressions, such as arithmetic and geometric progressions. In arithmetic progressions, the difference between consecutive terms is constant, while in geometric progressions, the ratio between consecutive terms is constant. To find the nth term in an arithmetic progression, you can use the formula an = a1 + (n-1)d, where a1 is the first term and d is the common difference between terms. The formula for finding the sum of an arithmetic progression is Sn = (n/2)(a1</

Jul 16, 2004

neenuroy

I need all formulas related to progressions...AP,GP,HP...all the formulas to find the sum of these progressions..Please i need it immediately

Mathematics news on Phys.org

Jul 16, 2004

hello3719

try deriving them.

Jul 16, 2004

Gokul43201

Staff Emeritus

Science Advisor

Gold Member

http://mathworld.wolfram.com/GeometricSeries.html
http://mathworld.wolfram.com/HarmonicSeries.html
http://mathworld.wolfram.com/ArithmeticSeries.html

1. What are progressions?

Progressions are sequences of numbers where there is a specific pattern or rule that determines the next term in the sequence. These patterns can involve arithmetic, geometric, or other types of sequences.

2. What is the difference between arithmetic and geometric progressions?

In arithmetic progressions, the difference between consecutive terms is constant. For example, in the sequence 2, 5, 8, 11, the difference between each term is 3. In geometric progressions, the ratio between consecutive terms is constant. For example, in the sequence 2, 6, 18, 54, the ratio between each term is 3.

3. How do you find the nth term in an arithmetic progression?

The formula for finding the nth term in an arithmetic progression is:
a_n = a₁ + (n-1)d
where a₁ is the first term in the sequence and d is the common difference between consecutive terms.

4. How do you find the sum of an arithmetic progression?

The formula for finding the sum of an arithmetic progression is:
S_n = (n/2)(a₁ + a_n)
where n is the number of terms in the sequence, a₁ is the first term, and a_n is the nth term.

5. What is the formula for finding the sum of a geometric progression?

The formula for finding the sum of a geometric progression is:
S_n = (a₁(1-rⁿ))/(1-r)
where a₁ is the first term and r is the common ratio between consecutive terms.