48,36,27,81/4...........

general term?

uh you mean pattern? well the 2nd is 3/4 of 48 and the 3rd is 3/4 of the 2nd. it is a geometric series with ratio 3/4 and first term a

To find the general term of a sequence, we need to look for a pattern or a rule that governs the sequence. Let's analyze the given sequence: 48, 36, 27, 81/4.

We can see that each term in the sequence is obtained by dividing the previous term by a specific number. In this case, each subsequent term is obtained by dividing the previous term by 4.

Starting with the first term, 48, we divide it by 4 to get the second term:
48 / 4 = 12

We then divide the second term, 12, by 4 to get the third term:
12 / 4 = 3

Continuing this pattern, we divide the third term, 3, by 4 to get the fourth term:
3 / 4 = 3/4

So, the fourth term of the sequence is 3/4.

We have established the rule that each term is obtained by dividing the previous term by 4. Using this pattern, we can determine the general term of the sequence.

Let's denote the general term as 'a(n)', where 'n' represents the position of the term in the sequence. In this case, 'n' starts at 1.
The first term, a(1), is 48.

To get the general term, we can express it as a function of the position 'n' and the previous term 'a(n-1)'. In this sequence, we divide the previous term by 4 to get the current term.

So, the general term can be defined as:
a(n) = a(n-1) / 4

Using this formula, we can calculate any term in the sequence. For example, to find the 5th term, we substitute 'n = 5' into the formula:
a(5) = a(4) / 4 = (3/4) / 4 = 3/16

Therefore, the general term of the given sequence is:
a(n) = a(n-1) / 4