# What's the last number in my wordy number sequence?

I have a wordy number sequence, partially shown below:

$${1, 45.2548, 1262.6650, 32768, 390625, 10077696, 282475249, 3037000499.976, 31381059609, ... }$$

Can you find the last number in the sequence?

Hint 1:

Look at the tags! Doesn't one seem odd?

Hint 2:

Look at the adjectives! Doesn't one seem odd?

Hint 3:

If you solve this puzzle, you will get 15 (power)points towards your reputation!

• Why "wordy"???? – IsaacRoan Sison Jun 29 at 6:11
• @IsaacRoanSison See my comment on the answer below... – Stiv Jun 29 at 8:03

Complete Solution:

The numbers can be rewritten as:

$$1=1^k$$
$$45.2548=2^{5.5}$$
$$1262.6650=3^{6.5}$$
$$32768=4^{7.5}$$
$$390625=5^{8}$$
$$10077696=6^{9}$$
$$282475349=7^{10}$$
$$3037000499.976=8^{10.5}$$
$$31381059609=9^{11}$$

Therefore, the $$n$$-th term should take the form of:

$$n^x$$

By Hint 3,

The author hints that the powers are actually consecutive font sizes in Microsoft Word! Thanks to @shoover in the comments for discovering the connection to font sizes! Also credit to @Stiv for finding the link between "Word" and MS Office first, though it was actually the hint gave it away to me.
The list of font sizes in the dropdown menu, in increasing order: 5 5.5 6.5 7.5 8 9 10 10.5 11 12 14 16 18 20 22 24 26 28 36 48 72 (largest font size in the dropdown menu).

Therefore, the last term is

the 21st term, and is equal to $$21^{72}$$ aka 158412417187039737963434604385921446947320760732675527347603818345931941295685218431561257343841

With that said, though, it should be noted:

There are actually two versions of list of font sizes in the dropdown menu! The version the @Ankit used seems to be extremely uncommon. The more common version, which is 8 9 10 11 12 14 16 18 20 22 24 26 28 36 48 72, is much more widely used. With this more common list of font sizes, it would have been impossible to spot the pattern!

Here is the screenshot of Word 2007 with the list of font sizes used in this problem (Source):

• good start; wasn't expecting anyone to catch the math so quickly. All the information needed is already there. Tbh I gave more terms than you would need. Pay attention to the words written there. Also be aware that you are supposed to find the last number, not the next one. – Ankit Jun 22 at 3:40
• I'm guessing the mathematical pattern followed quickly from a chance factoring of the integers present? – Feryll Jun 22 at 5:27
• Nice answer. To complete the solution we may look for hints in "wordy", but also in the fact that non-integers terms have not been rounded in the same way (I don't know whether it is relevant). – Evargalo Jun 22 at 9:26
• @Feryll That's right. – Jerry Dean Jun 22 at 9:41
• @Ankit I would agree that it's not a serious problem, but I did feel kind of frustrated while solving this, because at one point I was literally looking at every text editor available on the Net to find this list of fontsizes. Also, I think it's not a version issue, because I've seen screenshots of different word versions with either version of font sizes. Plus, it's actually quite difficult to look up the different versions (it could be that I'm doing it wrong). – Jerry Dean Jul 1 at 15:14