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
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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.Quote:
Originally Posted by sri340
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.
how would one find an nth term for this?
If $\displaystyle n$ is odd, nth term = $\displaystyle n$.Quote:
Originally Posted by Mukilab
If $\displaystyle n$ is even, call it $\displaystyle n=2k$.
Then it's just $\displaystyle 2^k$
