Given the function notation for the explicitly defined sequence f(n)=2^n−1

Question

, find the fifth term of the sequence.
why is 9 wrong and 16 the correct answer

Answer 1

To find the fifth term of the explicitly defined sequence given by the function \( f(n) = 2^n - 1 \), we need to evaluate the function at \( n = 5 \).

Let's compute \( f(5) \):

\[ f(5) = 2^5 - 1 \]

Calculating \( 2^5 \):

\[ 2^5 = 32 \]

Now, subtracting 1:

\[ f(5) = 32 - 1 = 31 \]

Thus, the fifth term of the sequence is 31.

Now, regarding the numbers 9 and 16:

• If someone suggested that the fifth term could be 9, perhaps they were mistakenly applying different values of \( n \):
  • \( f(4) = 2^4 - 1 = 16 - 1 = 15 \)
  • \( f(3) = 2^3 - 1 = 8 - 1 = 7 \)

None of these values equal 9.

• For 16, they might have confused the term with \( f(4) = 15\) and thought about \( 2^4 = 16\) and made an arithmetic mistake.

However, the correct calculation for \( f(5) \) clearly shows that the fifth term is 31, not 9 or 16.

If you meant 9 and 16 in relation to somewhere else, those could perhaps be relating to earlier terms or misinterpretations, but regarding the sequence defined by \( f(n) = 2^n - 1 \), the fifth term is 31.

Answer 2

NO THE CORRECT ANSWER IS 16

Answer 3

I apologize for the confusion in my previous response. Let me go through the sequence calculation again to clarify.

The function defined for the sequence is:

\[ f(n) = 2^n - 1 \]

To find the fifth term, we need to compute \( f(5) \):

\[ f(5) = 2^5 - 1 \]

Calculating \( 2^5 \):

\[ 2^5 = 32 \]

Now subtracting 1:

\[ f(5) = 32 - 1 = 31 \]

However, if you are referring to the fourth term \( f(4) \):

\[ f(4) = 2^4 - 1 \]

Calculating \( 2^4 \):

\[ 2^4 = 16 \]

Now subtracting 1:

\[ f(4) = 16 - 1 = 15 \]

Summary:

• The fifth term \( f(5) = 31 \).
• The fourth term \( f(4) = 15 \).

If there is a misunderstanding and you mean a certain context where the output would yield 16, please clarify, but according to \( f(n) = 2^n - 1 \), the calculations stand as shown.

Answer 4

2^(5-1)

Answer 5

Thank you for your patience and clarification.

If we calculate \( f(n) = 2^{n-1} \) instead of \( f(n) = 2^n - 1 \), then the fifth term would be calculated as follows:

\[ f(5) = 2^{5-1} = 2^4 \]

Calculating \( 2^4 \):

\[ 2^4 = 16 \]

So, under the revised function \( f(n) = 2^{n-1} \), the fifth term is indeed 16.

Thank you for bringing this to my attention, and I appreciate your understanding! If you have any further questions, please feel free to ask.