Sequences and Series Formulas
|
Arithmetic Progression |
Geometric Progression |
---|---|---|
Sequence |
a, (a + d), (a+2d), (a + 3d),………. | a, ar, ar2,ar3,…. |
Series |
a + (a + d) + (a + 2d) + (a + 3d) +… | a + ar + ar2 + ar3 +…. |
First term |
a | a |
Common Difference or Ratio |
Common difference = Successive term – Preceding term => d = a2 – a1 |
Common ratio = Successive term/Preceding term => r = ar(n-1)/ar(n-2) |
nth term |
a + (n-1)d | ar(n-1) |
Sum of first n terms |
Sn = (n/2)[2a + (n-1)d] |
Sn = a(1 – rn)/(1 – r) if r < 1 Sn = a(rn -1)/(r – 1) if r > 1 |
- The sum of the terms of an infinite geometric series is given by,
Sn = a/(1−r)
for |r| < 1, and not defined for |r| > 1
Also read: Types of Sequence
Sequences and Series Formulas
Sequences and Series Formulas: In mathematics, sequence and series are the fundamental concepts of arithmetic. A sequence is also referred to as a progression, which is defined as a successive arrangement of numbers in an order according to some specific rules. A series is formed by adding the elements of a sequence.
Let us consider an example to understand the concept of a sequence and series better. 1, 3, 5, 7, 9 is a sequence with five terms, while its corresponding series is 1 + 3 + 5 + 7 + 9, whose value is 25.
This article explores the sequences and series formulas, including arithmetic, geometric, and harmonic series.
Table of Content
- Sequence and Series Definition
- Types of Sequences and Series
- Arithmetic Sequence and Series
- Geometric Sequence and Series
- Harmonic Sequence and Series
- Fibonacci Numbers
- Sequences and Series Formulas
- Difference Between Sequences and Series
- Sequences and Series Formulas Examples