Algebra Equations with Progressions

Name:

Date:

Mathematical equations and number sequences

🌶️ Mild Level: Basic Equations & Simple Progressions

1. Solve for x: x + 7 = 15

2. Find the next two terms in this arithmetic progression: 3, 7, 11, 15, _____, _____

3. Solve for y: 3y = 21

4. Complete the pattern: 2, 5, 8, 11, _____, _____

What is the rule? Add _____ each time.

🌶️🌶️ Medium Level: Complex Equations & Geometric Progressions

5. Solve for x: 2x - 5 = 13

6. Find the next two terms in this geometric progression: 2, 6, 18, 54, _____, _____

What is the multiplier? _____

7. Solve for a: 4(a + 3) = 28

8. Which type of progression is this? Circle your answer.

Sequence: 1, 4, 16, 64, 256

Arithmetic progression

Geometric progression

🌶️🌶️🌶️ Spicy Level: Advanced Problems & Word Problems

9. Sarah saves money each week. In week 1, she saves $5. Each week after that, she saves $3 more than the previous week. How much will she save in week 6?

10. Solve for x: 3(2x - 4) + 7 = 25

11. A bacterial culture doubles every hour. If there are 8 bacteria at the start, write an equation to find the number of bacteria (N) after t hours, then calculate how many bacteria there will be after 5 hours.

Equation: N = _____________

12. Challenge: The sum of three consecutive numbers in an arithmetic progression is 27. If the middle number is x, write and solve an equation to find all three numbers.