Recursive vs Explicit Formulas Math Example 4

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

Example 4

easy
Write a recursive formula for 5,10,20,40,80,…5, 10, 20, 40, 80, \ldots

Solution

  1. 1
    Each term is double the previous; first term is 5.
  2. 2
    Recursive: a1=5a_1 = 5, an=2an−1a_n = 2a_{n-1}.

Answer

a1=5a_1 = 5; an=2an−1a_n = 2a_{n-1}
State the initial term and the recurrence. Both parts are required — a recursion without an initial condition is incomplete.

About Recursive vs Explicit Formulas

Two ways to define a sequence: recursive uses the previous term(s), explicit gives the nnth term directly as a function of nn.

Learn more about Recursive vs Explicit Formulas →

More Recursive vs Explicit Formulas Examples

Example 1 easy

A sequence is defined by [formula], [formula]. Find an explicit formula and compute [formula].

Example 2 medium

A sequence satisfies [formula], [formula]. Find the explicit formula and identify the growth type.

Example 3 medium

A sequence is defined by [formula], [formula]. Write the explicit formula and find [formula].

Example 5 medium

Convert [formula] to a recursive formula.

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