How to find the first four terms of the sequence

In mathematics, a sequence is an ordered list of objects. Accordingly, a number sequence is an ordered list of numbers that follow a particular pattern.

An ordered list of numbers is called a sequence. Each number of the sequence is called a term. The three dots represent that the sequence goes on to infinity. A sequence is called an arithmetic sequence if the difference between the two terms is constant. While observing the above example it can be easily identified that 3 is added to the first term of the sequence to get the second term and similarly adding 3 to the second term to get the third term and so on. Therefore, the rule for defining an arithmetic sequence will be as. In this example, we can observe that there is a difference between the two consecutive terms, that is -5, which is the common difference.

How to find the first four terms of the sequence

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The yearly salary values described form a geometric sequence because they change by a constant factor each year. Each term of a geometric sequence increases or decreases by a constant factor called the common ratio. The sequence below is an example of a geometric sequence because each term increases by a constant factor of 6. Multiplying any term of the sequence by the common ratio 6 generates the subsequent term. A geometric sequence is one in which any term divided by the previous term is a constant.

How to find the first four terms of the sequence

Many jobs offer an annual cost-of-living increase to keep salaries consistent with inflation. When a salary increases by a constant rate each year, the salary grows by a constant factor. In this section, we will review sequences that grow in this way. The yearly salary values described form a geometric sequence because they change by a constant factor each year. Each term of a geometric sequence increases or decreases by a constant factor called the common ratio. The sequence below is an example of a geometric sequence because each term increases by a constant factor of 6. Multiplying any term of the sequence by the common ratio 6 generates the subsequent term. A geometric sequence is one in which any term divided by the previous term is a constant.

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Please Login to comment Engineering Exam Experiences. Using the equation above, calculate the 8 th term:. How to Identify an Algebraic Expression? Using the same number sequence in the previous example, find the sum of the arithmetic sequence through the 5 th term:. Therefore, the rule for defining an arithmetic sequence will be as. Can a triangle and a square have the same perimeter? To find the first four terms of the above sequence, find a 1 , a 2 , a 3 , a 4 , a 5, i. A series is convergent if the sequence converges to some limit, while a sequence that does not converge is divergent. Easy Normal Medium Hard Expert.

A video game company launches an exciting new advertising campaign. They predict the number of online visits to their website, or hits, will double each day. The model they are using shows 2 hits the first day, 4 hits the second day, 8 hits the third day, and so on.

How to Identify an Algebraic Expression? Engineering Exam Experiences. Article Tags :. What is the probability of getting 7 on rolling a die? Create Improvement. Like Article. You can suggest the changes for now and it will be under the article's discussion tab. Comparing the value found using the equation to the geometric sequence above confirms that they match. How to find common ratio with first and last terms? Mathematically, the Fibonacci sequence is written as:. Using the equation above to calculate the 5 th term:. Suggest changes. Find the four consecutive integer numbers whose sum is 2. Admission Experiences. Get paid for your published articles and stand a chance to win tablet, smartwatch and exclusive GfG goodies!