Mathematics Exam > Mathematics Videos > Mathematics for Competitive Exams > Sequence of Real Numbers & Range of Sequence
Sequence of Real Numbers & Range of Sequence Video Lecture | Mathematics for Competitive Exams
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FAQs on Sequence of Real Numbers & Range of Sequence Video Lecture - Mathematics for Competitive Exams
| 1. What is a sequence of real numbers? |  |
Ans. A sequence of real numbers is an ordered list of real numbers, where each number is associated with a positive integer index. For example, a sequence can be written as (a₁, a₂, a₃, ...), where a₁, a₂, a₃, ... are real numbers in a specific order.
| 2. What is the range of a sequence? | |
Ans. The range of a sequence refers to the set of all values that appear in the sequence. It is the collection of all real numbers that are elements of the sequence. The range can be finite or infinite, depending on the sequence.
| 3. How can the terms of a sequence be determined? | |
Ans. The terms of a sequence can be determined by following a specific pattern or using a given formula. For example, if a sequence is defined by the formula an = 2n, the terms can be determined by substituting different values of n into the formula. In this case, the terms would be 2, 4, 6, 8, ...
| 4. Are all sequences of real numbers convergent? | |
Ans. No, not all sequences of real numbers are convergent. A sequence is said to be convergent if it approaches a specific limit as the index increases. However, there are sequences that do not approach any limit and are called divergent sequences. These sequences may oscillate or grow without bound.
| 5. How can the range of a sequence be determined? | |
Ans. To determine the range of a sequence, we need to list all the distinct values that appear in the sequence. This can be done by examining the terms of the sequence and identifying the unique values. The range will include all these distinct values in the order they appear in the sequence.
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