Write the first five terms of each sequence whose general term is given.

Question

a Subscript nequalsnothing2 Superscript n
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Part 1
a 1 equals nothing
  
​(Simplify your answer.Type an integer or​ fraction.)

Answer 1

The general term for the sequence is given as \( a_n = 2^n \).

To find the first five terms, we will substitute \( n = 1, 2, 3, 4, \) and \( 5 \) into the general term:

1. For \( n = 1 \):
   \( a_1 = 2^1 = 2 \)

2. For \( n = 2 \): \( a_2 = 2^2 = 4 \)

3. For \( n = 3 \): \( a_3 = 2^3 = 8 \)

4. For \( n = 4 \): \( a_4 = 2^4 = 16 \)

5. For \( n = 5 \): \( a_5 = 2^5 = 32 \)

Thus, the first five terms of the sequence are:

• \( a_1 = 2 \)
• \( a_2 = 4 \)
• \( a_3 = 8 \)
• \( a_4 = 16 \)
• \( a_5 = 32 \)

In summary, the first five terms are: 2, 4, 8, 16, 32.