Whether you use a football or a basketball, you will notice that the height at which it bounces tends to decrease every time it hits the ground. This decrease in the bouncing height is in a geometric sequence. Thus, it can be said that the geometric sequence is basically a sequence in which each term multiplies or divides by the same value from one specific term to the next one. The value by which a term divides or multiplies is known as the common ratio.
The difference between Arithmetic and Geometric Sequence is that while an arithmetic sequence has the difference between its two consecutive terms remains constant, a geometric sequence has the ratio between its two consecutive terms remains constant. The difference between two consecutive terms in an arithmetic sequence is referred to as the common difference. On the other hand, the ratio of two consecutive terms in a geometric sequence is referred to as the common ratio.
When you talk about arithmetic sequence or arithmetic progression, it basically refers to a sequence of different numbers in which the difference between 2 consecutive numbers is always constant. In this type of sequence, difference means the first term subtracted from the second term. If you consider a sequence such as 1, 4, 7, 10, 13…it is an arithmetic sequence in which the constant difference if 3. Just like anything else in mathematics, an arithmetic sequence also has a formula. It is important for you to know that the behavior of an arithmetic sequence depends a lot on the common difference.
However, if the common difference is negative, the terms will grow in a negative manner. The geometric sequence or geometric progression in mathematics happens to be a sequence of different numbers in which each new term after the previous is calculated by simply multiplying the previous term with a common ratio. Arithmetic Sequence refers to a list of numbers, in which the difference between successive terms is constant.
To put simply, in an arithmetic progression, we add or subtract a fixed, non-zero number, each time infinitely. If a is the first member of the sequence, then it can be written as:. In mathematics, the geometric sequence is a collection of numbers in which each term of the progression is a constant multiple of the previous term.
In finer terms, the sequence in which we multiply or divide a fixed, non-zero number, each time infinitely, then the progression is said to be geometric. Further, if a is the first element of the sequence, then it can be expressed as:. Example : 3, 9, 27, 81… 4, 16, 64, The following points are noteworthy so far as the difference between arithmetic and geometric sequence is concerned:. Hence, with the above discussion, it would be clear that there is a huge difference between the two types of sequences.
This tends to confuse a lot of students while sitting for their exams. Geometric sequences are exponential functions such that the n-value increases by a constant value of one and the f n value increases by multiples of r. The above comprehensive information about arithmetic and geometric sequence is quite enough to spearhead easier understanding.
However, these two sequences might appear similar in an examination setup and cause a lot of confusion. Doing more practise will help to resolve the problem. Calculating questions relating to arithmetic sequence are way simple but those of geometric sequence tend to pose a lot of challenges.
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