Always test to see if there is a common difference between terms (like added or subtracted), or a common ratio (multiplied or divided). Show Explanation:From 96 to 48, and from 48 to 24, and from 24 to 12, there is a consistent procedure of dividing by 2. (Multiplying by #1/2#) Continue to check subsequent terms to see if the pattern continues... 12 to 6, 6 to 3, etc. This sequence is geometric because of the pattern that you discovered! Arithmetic is a mathematical operation that deals with numerical systems and related operations. It’s used to get a single, definite value. The word “Arithmetic” comes from the Greek word “arithmos,” which meaning “numbers.” It is a field of mathematics that focuses on the study of numbers and the properties of common operations such as addition, subtraction, multiplication, and division. A sequence is a collection of items in a specific order (typically numbers). Arithmetic and geometric sequences are the two most popular types of mathematical sequences. Each consecutive pair of terms in an arithmetic sequence has a constant difference. A geometric sequence, on the other hand, has a fixed ratio between each pair of consecutive terms. Arithmetic SequenceIf the difference between any two consecutive terms is always the same, a sequence of integers is termed an Arithmetic Sequence. Simply put, it indicates that the next number in the series is calculated by multiplying the preceding number by a set integer. Further, an Arithmetic Sequence can be written as, a, a + d, a + 2d, a + 3d, a + 4d where a = the first term d = common difference between terms. For example, in the following sequence: 5, 11, 17, 23, 29, 35, …, the constant difference is 6. Geometric SequenceIf the ratio of any two consecutive terms is always the same, a sequence of numbers is called a Geometric Sequence. Simply put, it means that the next number in the series is calculated by multiplying a set number by the preceding number. Further, a Geometric Sequence can be expressed as: a, ar, ar2, ar3, ar4 … where a = first term d = common difference between terms. For instance, 2, 6, 18, 54, 162,… The constant multiplier is 3 in this case. How can you tell the difference between an Arithmetic sequence and a Geometric sequence?To tell the difference between arithmetic and geometric sequence, the following points are important,
Difference between an arithmetic sequence and a geometric sequence
Sample ProblemsQuestion 1: What is a Geometric Sequence, and why is it called that? Answer:
Question 2: Is it possible for an Arithmetic Sequence to also be Geometric? Answer:
Question 3: In an arithmetic sequence, what is ‘a’? Answer:
Question 4: What is the procedure for determining the nth term of an arithmetic sequence? Answer:
Question 5: What is the procedure for determining the nth term of a geometric sequence? Answer:
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