Repeated Operations Math Example 4

Follow the full solution, then compare it with the other examples linked below.

Example 4

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

Solution

  1. 1
    1st: 1.
  2. 2
    2nd: \(1 \times 3 = 3\).
  3. 3
    3rd: \(3 \times 3 = 9\).
  4. 4
    4th: \(9 \times 3 = 27\).
  5. 5
    5th: \(27 \times 3 = 81\).

Answer

81
Repeated multiplication by 3 gives powers of 3: 1, 3, 9, 27, 81. The 5th term is \(3^4 = 81\).

About Repeated Operations

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

Learn more about Repeated Operations →

More Repeated Operations Examples

Example 1 easy

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

Example 2 medium

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

Example 3 easy

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

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