Find the next term of the sequence:
2, 10,50,250,1250,
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Find the next term of the sequence: 2, 10,50,250,1250, Question Help: $$ \square $$ Video Submit Question

UpStudy AI · Accepted Answer

To determine the next term in the sequence **2, 10, 50, 250, 1250, ...**, let's analyze the pattern step by step.

### Observing the Pattern

1. **First Term:** 2
2. **Second Term:** 10
   - **Calculation:** $$ 2 \times 5 = 10 $$
3. **Third Term:** 50
   - **Calculation:** $$ 10 \times 5 = 50 $$
4. **Fourth Term:** 250
   - **Calculation:** $$ 50 \times 5 = 250 $$
5. **Fifth Term:** 1250
   - **Calculation:** $$ 250 \times 5 = 1250 $$

### Identifying the Rule

From the above calculations, it's evident that **each term is obtained by multiplying the previous term by 5**.

### Calculating the Next Term

Following the identified pattern:

- **Next Term:** $$ 1250 \times 5 = 6250 $$

### General Formula

If you want a general formula to find the $$ n^{th} $$ term of this sequence, you can use:

$$
a_n = 2 \times 5^{(n-1)}
$$

- **Where:**
  - $$ a_n $$ is the $$ n^{th} $$ term.
  - $$ n $$ is the position of the term in the sequence.

**Example:**

- For $$ n = 6 $$:
  $$
  a_6 = 2 \times 5^{(6-1)} = 2 \times 3125 = 6250
  $$

### **Answer:**  
The next term in the sequence is **6250**.
The next term in the sequence is 6250.

Find the next term of the sequence:
2, 10,50,250,1250,
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Find the next term of the sequence:
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