sequence is an ordered list of numbers. The numbers in the list are the terms of the sequence. A series is the addition of all the terms of a sequence. Sequence and series are similar to sets but the difference between them is in a sequence, individual terms can occur repeatedly in various positions. The length of a sequence is equal to the number of terms, which can be either finite or infinite. Let us start learning Sequence and series formula.
Sequence and Series Formula
What are Sequence and Series?
A sequence is an ordered list of numbers. The numbers in the list are the terms of the sequence. The terms of a sequence usually name as ai or an, with the subscripted letter i or n being the index. So, the second term of a sequence might be named a2, and a12 would be the twelfth term.
A series termed as the sum of all the terms in a sequence. However, there has to be a definite relationship between all the terms of the sequence.
SN = a1+a2+a3 + .. + an
Types of Sequence and Series
Sequences: A finite sequence stops at the end of the list of numbers like a1, a2, a3, a4, a5, a6
an. whereas, an infinite sequence is never-ending i.e. a1, a2, a3, a4, a5, a6
an
..
Series: In a finite series, a finite number of terms are written like a1 + a2 + a3 + a4 + a5 + a6 +
an. In case of an infinite series, the number of elements are not finite i.e. a1 + a2 + a3 + a4 + a5 + a6 +
an +
..
Some Common Sequences
Arithmetic Sequences:
A sequence in which every term is obtained by adding or subtraction a definite number to the preceding number is an arithmetic sequence.
Geometric Sequences:
A sequence in which every term is obtained by multiplying or dividing a definite number with the preceding number is known as a geometric sequence.
Harmonic Sequences:
If the reciprocals of all the elements of the sequence form an arithmetic sequence then the series of numbers is said to be in a harmonic sequence
