https://r2.erweima.ai/mathbot/image/1725853952214vs8o3oq6.pdf

The document contains a series of math exercises involving sequences and equations. Below is an overview of each section:

### Ejercicio 1: Sequences
- Identify the next three terms in two sequences:
  a) 590, 577, 564, 551, …
  b) 730, 745, 760, 775, …

### Ejercicio 2: Terms in a Sequence
- Calculate the 80th, 105th, and 130th terms for several sequences given by different formulas.

### Ejercicio 3: Sequence Length
- Determine the total number of terms in two arithmetic sequences:
  a) 11, 16, 21, 26, ..., 166
  b) 1, 6, 11, ..., 111

### Ejercicio 4: Arithmetic Sequences
- Solve questions about arithmetic sequences, including the number of terms required for a certain sum and finding the full sequence.

### Ejercicio 5: Geometric Sequences
- Find the first five terms of several geometric sequences.

### Ejercicio 6: Linear Equations
- Solve a series of linear equations step by step.

### Ejercicio 7: Quadratic Equations
- Solve quadratic equations step by step.

Would you like to solve any specific exercise, or have a detailed breakdown of one of these topics?

Here are 5 follow-up questions for further exploration:
1. How do you find the common difference in an arithmetic sequence?
2. How do you calculate the sum of an arithmetic sequence?
3. What is the general formula for the nth term in a geometric sequence?
4. How can you solve a quadratic equation by factoring?
5. What steps are involved in solving linear equations with variables on both sides?

**Tip**: When solving quadratic equations, always check if factoring is possible before using the quadratic formula to save time!

The document contains a series of math exercises involving sequences and equations. Below is an overview of each section:

### Ejercicio 1: Sequences
- Identify the next three terms in two sequences:
  a) 590, 577, 564, 551, …
  b) 730, 745, 760, 775, …

### Ejercicio 2: Terms in a Sequence
- Calculate the 80th, 105th, and 130th terms for several sequences given by different formulas.

### Ejercicio 3: Sequence Length
- Determine the total number of terms in two arithmetic sequences:
  a) 11, 16, 21, 26, ..., 166
  b) 1, 6, 11, ..., 111

### Ejercicio 4: Arithmetic Sequences
- Solve questions about arithmetic sequences, including the number of terms required for a certain sum and finding the full sequence.

### Ejercicio 5: Geometric Sequences
- Find the first five terms of several geometric sequences.

### Ejercicio 6: Linear Equations
- Solve a series of linear equations step by step.

### Ejercicio 7: Quadratic Equations
- Solve quadratic equations step by step.

This resource provides step-by-step solutions to arithmetic and geometric sequences, as well as linear and quadratic equations. Students will learn how to find sequence terms, calculate sums, and solve equations with detailed instructions and key formulas.

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