Question

Writeanequationtodescribethesequencebelow.Usentorepresentthepositionofaterminthesequence,wheren = 1forthefirstterm.


1 , 2 , 4 , ...
Write your answer using decimals and integers


an = _(_)^ n^ -^ 1
Answer
answer aghain
tyou left a space blank
Answered by GPT-4o mini
The sequence you provided is: 1, 2, 4, ...

This sequence can be identified as a geometric sequence where each term is multiplied by 2 to find the next term.

To write an equation for the \( n \)-th term of this sequence, we observe the following:

- The first term \( a_1 = 1 \) can be represented as \( 2^0 \).
- The second term \( a_2 = 2 \) can be represented as \( 2^1 \).
- The third term \( a_3 = 4 \) can be represented as \( 2^2 \).

From this observation, we can write the general formula for the \( n \)-th term (\( a_n \)) of the sequence:

\[
a_n = 2^{n-1}
\]

Thus, the equation to describe the sequence is:

\[
a_n = 2^{n - 1}
\]
Answered by GPT-4o mini
I apologize for the oversight. The formula for the sequence can be filled in as follows:

\[
a_n = 2^{(n - 1)}
\]

So, if you're looking for the answer structured as requested in your previous message, it would be:

\[
a_n = 2^{(n - 1)}
\]

Again, I'm sorry for the confusion!