Yes, a common ratio in a geometric sequence can definitely be a decimal.
A geometric sequence is a sequence where each term is multiplied by a constant value, called the common ratio, to obtain the next term. This common ratio can be any real number, including decimals, positive numbers, negative numbers, whole numbers, and fractions.
Examples of Geometric Sequences with Decimal Common Ratios:
- Sequence 1: 2, 1, 0.5, 0.25, 0.125... (Common ratio = 0.5)
Each term is multiplied by 0.5 (which is a decimal) to get the next term. - Sequence 2: 5, 1.5, 0.45, 0.135... (Common ratio = 0.3)
Each term is multiplied by 0.3 (which is a decimal) to get the next term. - Sequence 3: 1, -0.2, 0.04, -0.008... (Common ratio = -0.2)
The common ratio can also be a negative decimal.
Why Decimal Common Ratios Work
The common ratio simply represents the factor by which each term changes. Decimals, like 0.5 (which is equivalent to 1/2), simply imply a fractional scaling of the sequence's terms. Therefore, there are no restrictions preventing the common ratio from being a decimal value.
In conclusion, a common ratio in a geometric sequence can absolutely be a decimal.
