Answer:
Step-by-step explanation:
We will find that the recursive relation for the sequence is:
How to determine a given sequence?
There is not a straightforward way of determining a sequence, we just need to try to see a pattern.
For example, if we analyze the first 3 terms:
3, 5, 12
We can see that the third number is equal to the product of the first two minus the first one:
3*5 - 3 = 15 - 3 = 12
Now let's see if this pattern remains true for any other set of 3 consecutive terms:
for 5, 12, 55 we have:
5*12 - 5 = 60 - 5 = 55
So the pattern remains.
Now let's see for the last 3.
12, 55, 648.
12*55 - 12 = 660 - 12 = 648
The pattern remains.
Then we can write a recursive relation as:
And because this relation depends on the two previous terms, we also need to specify the first two terms of the sequence, so we have:
If you want to learn more about sequences, you can read:
