I am sure every one of you must be having your piggy banks. So, suppose you put Rs 100 today in your piggy bank. Next day you put Rs 10. Again on the third day, you put Rs 10. So in this way every day, you keep on adding Rs 10 in your piggy bank. What if one day you want to know the total amount of money in your bank? So here you use the sequence. Such kind of ordered list is known as the sequence. And the sequence if presented as the sum of the list items, is known as series. Let us now study in detail about Sequence and Series.
- Introduction to Sequences and Series
- Arithmetic Progression
- Geometric Progression
- Means
- Special Series
FAQs on Sequences and Series
Question 1: Explain what is a sequence with example?
Answer: A sequence refers to an ordered list of numbers. The three dots means that the sequence will continue forward in the established pattern. Term refers to each number in the sequence. For example, consider the sequence 1, 3, 5, 7, 9, …, here 1 happens to be the first term, 3 is the second term, the third term is 5, and so on.
Question 2: Explain the two types of sequences?
Answer: The two types of sequences are the arithmetic sequence and geometric sequence. Arithmetic sequence is the one in which the difference exists between two consecutive terms constant. This difference is referred to as the common difference. In contrast, the geometric sequence is the one that deals with the ratio between two consecutive terms constant.
Question 3: Is it necessary for a sequence to begin at 0 or 1?
Answer: It is not necessary for a sequence to begin at 0 or 1. A sequence can begin with any number.
Question 4: What is meant by real sequence?
Answer: A real sequence is the one whose codomain happens to be a set of real numbers R.