describe geometric sequence and give 2 example of geometric sequence
Answers
In mathematics, a geometric progression, also known as a geometric sequence, is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio. For example, the sequence 2, 6, 18, 54, ... is a geometric progression with common ratio 3.
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Answer:
In mathematics, a geometric progression, also known as a geometric sequence, is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio. For example, the sequence 2, 6, 18, 54, ... is a geometric progression with common ratio 3. Similarly 10, 5, 2.5, 1.25, ... is a geometric sequence with common ratio 1/2.
Diagram illustrating three basic geometric sequences of the pattern 1(rn−1) up to 6 iterations deep. The first block is a unit block and the dashed line represents the infinite sum of the sequence, a number that it will forever approach but never touch: 2, 3/2, and 4/3 respectively.
Examples of a geometric sequence are powers rk of a fixed number r, such as 2k and 3k. The general form of a geometric sequence is
{\displaystyle a,\ ar,\ ar^{2},\ ar^{3},\ ar^{4},\ \ldots } a,\ ar,\ ar^{2},\ ar^{3},\ ar^{4},\ \ldots
where r ≠ 0 is the common ratio and a is a scale factor, equal to the sequence's start value.