1. ## sequence

What is the next number in the sequence: 1, 2, 3, 4, 5, 8, 7, 16, 9, ...?

(A) 8 (B) 11 (C) 18 (D) 23 (E) 32

2. Originally Posted by sri340
What is the next number in the sequence: 1, 2, 3, 4, 5, 8, 7, 16, 9, ...?

(A) 8 (B) 11 (C) 18 (D) 23 (E) 32
While I'm sure you could justify any answer the one here is 32.

Why?

Write the sequence like this...

$\begin{array}{|c|c|c|c|c|c|c|c|c|c|c|}
Term & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\
Value & 1 & 2 & 3 & 4 & 5 & 8 & 7 & 16 & 9 & ?
\end{array}$

Now look at ONLY the odd terms. What can you say about them?

$\begin{array}{|c|c|c|c|c|c|}
Term & 1 & 3 & 5 & 7 & 9 \\
Value & 1 & 3 & 5 & 7 & 9
\end{array}$

Then look at the even terms.

$\begin{array}{|c|c|c|c|c|c|}
Term & 2 & 4 & 6 & 8 & 10 \\
Value & 2 & 4 & 8 & 16 & ?
\end{array}$

It seems to be increasing...But by how much each time.

3. how would one find an nth term for this?

4. Originally Posted by Mukilab
how would one find an nth term for this?
If $n$ is odd, nth term = $n$.

If $n$ is even, call it $n=2k$.

Then it's just $2^k$