Question

Sequence

3,5,12,55,648,?

Answer 1

We will find that the recursive relation for the sequence is:

$A_N = A_{N-1}*A_{N-2} - A_{N-2}\\A_1 = 3\\A_2 = 5$

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:

$A_N = A_{N-1}*A_{N-2} - A_{N-2}$

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:

$A_N = A_{N-1}*A_{N-2} - A_{N-2}\\A_1 = 3\\A_2 = 5$

If you want to learn more about sequences, you can read:

https://brainly.com/question/7882626