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MATH / The sequence 1, 2, 4, 5, 10, 11, 22, 23, 46, 47, … is formed as follows:

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problem

The sequence 1, 2, 4, 5, 10, 11, 22, 23, 46, 47, …\dots is formed as follows: •\bullet Start with the number 1. •\bullet Add one to get 2. •\bullet Double that to get 4. •\bullet Add one to get 5. •\bullet Double that to get 10, and so on. We repeat the steps of "add one" and "double that", alternating between them. The 100th term will be of the form 3⋅2k−1.3 \cdot 2^k - 1. Compute k.k.
Plain-text mathematical notation (without MathML)
The sequence 1, 2, 4, 5, 10, 11, 22, 23, 46, 47, … is formed as follows:

• Start with the number 1.

• Add one to get 2.

• Double that to get 4.

• Add one to get 5.

• Double that to get 10, and so on.

We repeat the steps of "add one" and "double that", alternating between them.

The 100th term will be of the form 3⋅2^(k)−1.  Compute k.
Original LaTeX notation
The sequence 1, 2, 4, 5, 10, 11, 22, 23, 46, 47, $\dots$ is formed as follows:

$\bullet$ Start with the number 1.

$\bullet$ Add one to get 2.

$\bullet$ Double that to get 4.

$\bullet$ Add one to get 5.

$\bullet$ Double that to get 10, and so on.

We repeat the steps of "add one" and "double that", alternating between them.

The 100th term will be of the form $3 \cdot 2^k - 1.$  Compute $k.$

level

Level 4

type

Intermediate Algebra

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Source and history

task_id
c534e197-394a-5e09-bee6-02362bb3dca5
task_key
intermediate~5falgebra--test--c534e197-394a-5e09-bee6-02362bb3dca5
task_revision_id
1
config / split
intermediate_algebra / test

Official source

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