Question
What is the next term in sequence? 1 3, 7, 15, 31........
Answers
GPT-4o mini
To find the next term in the sequence \(1, 3, 7, 15, 31\), let's first look for a pattern.
We can observe the following:
- The first term is \(1\).
- The second term is \(3 = 2 \times 1 + 1\).
- The third term is \(7 = 2 \times 3 + 1\).
- The fourth term is \(15 = 2 \times 7 + 1\).
- The fifth term is \(31 = 2 \times 15 + 1\).
From this, we can see that each term can be expressed as:
\[
a_n = 2 \cdot a_{n-1} + 1
\]
where \(a_1 = 1\).
Now, let's calculate the next term (\(a_6\)) using this pattern:
\[
a_6 = 2 \cdot a_5 + 1 = 2 \cdot 31 + 1 = 62 + 1 = 63
\]
Thus, the next term in the sequence is \(63\).
We can observe the following:
- The first term is \(1\).
- The second term is \(3 = 2 \times 1 + 1\).
- The third term is \(7 = 2 \times 3 + 1\).
- The fourth term is \(15 = 2 \times 7 + 1\).
- The fifth term is \(31 = 2 \times 15 + 1\).
From this, we can see that each term can be expressed as:
\[
a_n = 2 \cdot a_{n-1} + 1
\]
where \(a_1 = 1\).
Now, let's calculate the next term (\(a_6\)) using this pattern:
\[
a_6 = 2 \cdot a_5 + 1 = 2 \cdot 31 + 1 = 62 + 1 = 63
\]
Thus, the next term in the sequence is \(63\).