Drag and drop the sequences into the boxes to classify them as Arithmetic, Geometric, or Neither. $$ \frac{1}{2}, 1,2,3,4, \ldots $$ $$ \frac{5}{9}, \frac{5}{3}, 5,15,45, \ldots $$

Question

UpStudy AI · Accepted Answer

To classify the given sequences:

1. **Sequence 1:** $$\frac{1}{2}, 1, 2, 3, 4, \ldots$$

This sequence increases by a constant difference of $$ \frac{1}{2} $$ (from $$\frac{1}{2}$$ to $$1$$, $$1$$ to $$2$$, $$2$$ to $$3$$, and so on). Therefore, this sequence is classified as **Arithmetic**.

2. **Sequence 2:** $$\frac{5}{9}, \frac{5}{3}, 5, 15, 45, \ldots$$

To determine if this sequence is geometric, we can check the ratio between consecutive terms:
   - $$\frac{\frac{5}{3}}{\frac{5}{9}} = \frac{5}{3} \cdot \frac{9}{5} = 3$$
   - $$\frac{5}{15} = \frac{5}{3} \cdot \frac{3}{1} = 3$$
   - $$\frac{15}{5} = 3$$
   - $$\frac{45}{15} = 3$$

Since the ratio between consecutive terms is constant (equal to $$3$$), this sequence is classified as **Geometric**.

So, the classifications are:

- **Arithmetic:** $$\frac{1}{2}, 1, 2, 3, 4, \ldots$$
- **Geometric:** $$\frac{5}{9}, \frac{5}{3}, 5, 15, 45, \ldots$$
- **Arithmetic:** $$\frac{1}{2}, 1, 2, 3, 4, \ldots$$ - **Geometric:** $$\frac{5}{9}, \frac{5}{3}, 5, 15, 45, \ldots$$

Drag and drop the sequences into the boxes to classify them as Arithmetic, Geometric, or Neither. \[ \frac{1}{2}, 1,2,3,4, \ldots \] \( \frac{5}{9}, \frac{5}{3}, 5,15,45, \ldots \)

Solución de inteligencia artificial de Upstudy

Responder

Solución

The Deep Dive

preguntas relacionadas

Latest Arithmetic Questions