Repeated Operations Examples in Math

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Repeated Operations.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.

Concept Recap

Applying the same operation multiple times in succession, where the repetition is often compressed into a higher-level operation: repeated addition becomes multiplication (n \cdot a), and repeated multiplication becomes exponentiation (a^n).

Adding 5 three times: 5+5+5 = 3 \times 5. Multiplying 2 four times: 2 \times 2 \times 2 \times 2 = 2^4.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Repetition of an operation often leads to a more compact notation.

Common stuck point: Extension to non-integer repetitions requires new definitions.

Sense of Study hint: Write each repetition on a separate line and count how many times you applied the operation before simplifying.

Worked Examples

Example 1

easy
Start at 3 and add 4 repeatedly. Write the first 5 results.

Solution

  1. 1
    Start: 3.
  2. 2
    After 1st addition: \(3 + 4 = 7\).
  3. 3
    After 2nd: \(7 + 4 = 11\).
  4. 4
    After 3rd: \(11 + 4 = 15\).
  5. 5
    After 4th: \(15 + 4 = 19\).

Answer

3, 7, 11, 15, 19
Repeated addition of a constant creates an arithmetic sequence. Each term is 4 more than the previous.

Example 2

medium
Start with 2 and repeatedly double it. What are the first 5 values? What operation are you applying each time?

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy
Start at 50 and subtract 7 repeatedly. Write the first 4 results.

Example 2

medium
Start with 1 and multiply by 3 repeatedly. What is the 5th value in the sequence?
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Background Knowledge

These ideas may be useful before you work through the harder examples.

additionmultiplication