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In a sequence defined by a_n = 2^n, what is the value of a_5?

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Question: In a sequence defined by a_n = 2^n, what is the value of a_5?

Options:

  1. 32
  2. 16
  3. 64
  4. 8

Correct Answer: 32

Solution: 

a_5 = 2^5 = 32.

In a sequence defined by a_n = 2^n, what is the value of a_5?

Practice Questions

Q1
In a sequence defined by a_n = 2^n, what is the value of a_5?
  1. 32
  2. 16
  3. 64
  4. 8

Questions & Step-by-Step Solutions

In a sequence defined by a_n = 2^n, what is the value of a_5?
  • Step 1: Identify the formula for the sequence, which is a_n = 2^n.
  • Step 2: Determine the value of n for which we want to find a_n. In this case, n = 5.
  • Step 3: Substitute n = 5 into the formula: a_5 = 2^5.
  • Step 4: Calculate 2^5. This means multiplying 2 by itself 5 times: 2 * 2 * 2 * 2 * 2.
  • Step 5: Perform the multiplication: 2 * 2 = 4, then 4 * 2 = 8, then 8 * 2 = 16, and finally 16 * 2 = 32.
  • Step 6: Conclude that a_5 = 32.
  • Exponential Sequences – Understanding how to evaluate terms in a sequence defined by an exponential function.
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