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...
$\displaystyle \begin{array}{|c|c|c|c|c|c|c|c|c|c|c|}
Term & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\
Value & 1 & 2 & 3 & 4 & 5 & 8 & 7 & 16 & 9 & ?
\end{array}$
Now look at ONLY the odd terms. What can you say about them?
$\displaystyle \begin{array}{|c|c|c|c|c|c|}
Term & 1 & 3 & 5 & 7 & 9 \\
Value & 1 & 3 & 5 & 7 & 9
\end{array}$
Then look at the even terms.
$\displaystyle \begin{array}{|c|c|c|c|c|c|}
Term & 2 & 4 & 6 & 8 & 10 \\
Value & 2 & 4 & 8 & 16 & ?
\end{array}$
It seems to be increasing...But by how much each time.