Write a program to generate the following series. accept N from User:
1. 4, 16, 36, 64, --. N
2. 1, 2, 3, 4, 5, 6, ...N
3. 1, 4, 27, 256, 3125, --.N
Answers
Answer:
As all the other terms are of the form n^n, the next term *might* be 6^6, i.e. 46,656. I say “might” because, technically, we cannot know if the arguably more obvious n^n pattern is indeed that which gives the first several terms you have listed. For all we know the sequence might only *resemble* this pattern for up to n=5.
Given the relative simplicity of the sequence thus far, however, I am guessing such deeper issues are not being considered at this stage.
If you are nevertheless curious about how this ambiguity could arise, take, for example, the sequence:
1, 2, 3, … .
Perhaps our most immediate guess would be that the above is the sequence of Natural numbers in their usual, i.e. nondecreasing, order.
Not having shared how I derived those first few terms, however, you might just as well guess that I am listing the famous Fibonacci sequence, only omitting its usual first term, i.e
(1,) 1, 2, 3, 5, 8, 13, … .
Other, perhaps even more plausibly, easily misidentifiable sequences are as abundant as much as they can be relatively straightforward to contrive.
But, again, it is generally safe to assume a sequence is what it would first seem throughout most of the pre-university mathematics curricula, at least as I have seen it in the US.
If that, or the equivalent, is your situation, I would recommend answering the question with 46,656, as opposed to “not enough information” or the like. For, though the latter response is more accurate, it could also be misinterpreted by, say, your teacher.
That said, after officially giving the former answer, the latter could make for a nice discussion with your teacher, provided that you present it with an appropriate demeanor. Only being able to speak for myself, I know I would appreciate such an insight from one of my students!