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Algebra Equations with Progressions

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Algebra Equations with Progressions

Solve each equation and complete each progression. Show your working for the longer problems.

Core Skills

1.Find the value of x: x + 9 = 17.

2.Write the next two terms in this arithmetic progression: 5, 9, 13, 17, __, __.

3.Solve for y: 5y = 35.

4.Complete the arithmetic pattern: 4, 10, 16, 22, __, __. State the amount added each time.

Build on the Pattern

5.Solve for x: 3x − 8 = 16.

6.Find the next two terms in this geometric progression: 3, 12, 48, 192, __, __. What number is each term multiplied by?

7.Solve for a: 5(a + 2) = 40.

8.Is 2, 10, 50, 250 an arithmetic progression or a progression with a constant multiplier?

Arithmetic progression
Progression with a constant multiplier

Apply Your Algebra

9.Hugo puts $4 into a savings jar in the first week. Each week she saves $5 more than she saved the week before. How much does she put in during week 7?

10.Solve for x: 4(2x − 3) + 5 = 33.

11.A pond has 6 water lilies at the start. The number of lilies triples each week. Write a rule for the number, N, after t weeks, then use it to find the number after 4 weeks.

12.Three consecutive terms in an arithmetic progression add to 42. If the middle term is x, write an equation to find x. Explain why the outer terms cannot be uniquely determined from the information given.