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

Quote:

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.

how would one find an nth term for this?

Quote:

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 $2^k$