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Carrying Out the Plan

Explore how to implement a problem-solving plan involving geometric sequences. Understand the application of 2 to the power of n in calculating outcomes such as messages from bulbs, and see how geometric progressions model real-life phenomena like compound interest, population, and bacterial growth. This lesson helps you apply mathematical formulas to solve complex problems effectively.

Applying the solution

Let’s execute the plan we made in the previous step.

We want to calculate the number of messages with 10 bulbs. Now, let’s apply the formula to calculate it.

Number of messages with 10 bulbs=210=1024 messages\text{Number of messages with 10 bulbs} = 2^{10} = 1024 \text{ messages} ...