I Bet You Can’t Guess the Next Value in the Sequence…

**Guest post by Luke Westbrook**

Do you remember back in high school, even so far back as elementary school, taking those standardized tests? Inevitably, in the math portion of whatever test, there would be at least one question in which the first few numbers of a sequence were shown, and you had to determine what the next number was in the sequence. Remember those?

It’s been quite some time since I’ve taken one of those tests, but I don’t remember being particularly intimidated by them. You just had to figure out the pattern. Simple. Well, in honor of those “simple” standardized test questions, we decided to test your pattern recognition. But I bet you can’t guess the pattern this time.

Here it is. Determine, if you dare, the next number of the following sequence:

1, 3, 5, 7, …

Pretty easy, right? I mean, come on! It’s so obvious. The next number is clearly 217,341.

If you’re confused, good. You know, in retrospect, this would have been a good blog for April Fool’s Day. Oh well.

Allow me to explain, using PTC Mathcad, of course.

You see, the sequence given above is not consecutive odd numbers, as it would appear to be, but rather the outputs of consecutive integer inputs of the following equation:


If we evaluate the consecutive integer inputs, we get:


And just for kicks, let’s look at the plot of this function.


So there you go. The proper progression to the sequence given above is

1, 3, 5, 7, 217341, 1086671, 3259993, …

Still don’t believe me? Try it out for free with PTC Mathcad Express.