GMAT Exam > GMAT Videos > Quantitative for GMAT > Sequence Definition
Sequence Definition Video Lecture | Quantitative for GMAT
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FAQs on Sequence Definition Video Lecture - Quantitative for GMAT
| 1. What is a sequence in mathematics? |  |
A sequence in mathematics is a list of numbers that follow a specific pattern or rule. Each number in the sequence is called a term, and the position of a term in the sequence is referred to as its index. Sequences can be finite, where they have a specific number of terms, or infinite, where they continue indefinitely.
| 2. What is the difference between an arithmetic sequence and a geometric sequence? | |
In an arithmetic sequence, each term is obtained by adding a constant difference to the previous term. For example, the sequence 2, 5, 8, 11, 14 is an arithmetic sequence with a common difference of 3.
On the other hand, a geometric sequence is formed by multiplying each term by a constant ratio to obtain the next term. For example, the sequence 3, 6, 12, 24, 48 is a geometric sequence with a common ratio of 2.
| 3. How can we find the nth term of an arithmetic sequence? | |
To find the nth term of an arithmetic sequence, we can use the formula: an = a1 + (n - 1)d, where an represents the nth term, a1 is the first term, n is the position of the term, and d is the common difference.
For example, in the arithmetic sequence 2, 5, 8, 11, 14, if we want to find the 6th term, we can use the formula: a6 = 2 + (6 - 1)3 = 2 + 15 = 17.
| 4. How can we find the sum of an arithmetic sequence? | |
To find the sum of an arithmetic sequence, we can use the formula: Sn = (n/2)(a1 + an), where Sn represents the sum of the first n terms, a1 is the first term, and an is the nth term.
For example, in the arithmetic sequence 2, 5, 8, 11, 14, if we want to find the sum of the first 5 terms, we can use the formula: S5 = (5/2)(2 + 14) = 5(16) = 80.
| 5. What are some real-life applications of sequences? | |
Sequences have various real-life applications, such as in finance, physics, and computer science. In finance, sequences are used to calculate compound interest or analyze investment growth. In physics, sequences help describe natural phenomena, such as the Fibonacci sequence in modeling the growth of plants. In computer science, sequences are used in algorithms and data structures for tasks like sorting and searching.
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Dec 18, 2024 Last updated |
Video Description: Sequence Definition for GMAT 2024 is part of Quantitative for GMAT preparation.
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