In our day-to-day activities, we see different patterns, such as things that are placed in a particular order following a particular set of rules. For example, we can have 1, 3, 5, 7, … and 1, 2, 4, 8, … each representing a pattern. How do you find the next number in each pattern?

In the pattern 1, 3, 5, 7, … we find the next number by adding 2 to the preceding number and multiplying by 2 in the second pattern. We can also have a pattern of type 1, 4, 7, 10, …, or 1, 1/3, 1/9, 1/27, …; or other types possessing different rules.

A sequence is a group or sequential arrangement of numbers in a particular order or set of rules. A sequence can be finite or infinite. For example, 1, 2, 3, 4 is a finite sequence having four terms, whereas 1, 2, 3, 4, … is an infinite sequence.

There are various types of sequences depending upon the set of rules that are used to form the sequence. The type of sequence as in Example 1 determined by adding a fixed number is known as an arithmetic sequence. The sequence determined by multiplying a term by a fixed number is called a geometric sequence.

Though there are different types of sequences, in this unit we will focus on arithmetic sequences obtained by adding a fixed number to the preceding term and geometric sequences obtained by multiplying the preceding term by a fixed number respectively.

Beyond identifying the type of a sequence, we will study how to find the nth term and the sum of the first n-terms of a sequence.

In the above sequence, you can see that to obtain the next term, we will add 2 to the preceding term.

In this unit, we will focus on sequences obtained by:

• Adding a fixed number on the preceding term.
• Multiplying the preceding term by a fixed number.

Such sequences which are called arithmetic sequences and geometric sequences will be discussed. We will also study how to find the n^th term and the sum of the first n-terms of such sequences.