Analyze the Sequence: Finding the Pattern in 768, 192, 48, 12, 3

Question

Is there a rule to the following sequence? If so, then what is it?

768 , 192 , 48 , 12 , 3

Video Solution

Solution Steps

00:00 Is there a pattern, and if so, what is it?
00:04 We can see that the second term is 4 times larger than the first term
00:13 The same pattern exists between the third and second terms
00:22 And continues this way for all terms
00:35 Therefore, there is a pattern: each term is 4 times larger than the previous one
00:39 And this is the solution to the question

Step-by-Step Solution

Let's analyze the sequence: 768,192,48,12,3768, 192, 48, 12, 3.

First, observe the relationship between consecutive terms by dividing one term by the previous term:

  • 192768=14\frac{192}{768} = \frac{1}{4}
  • 48192=14\frac{48}{192} = \frac{1}{4}
  • 1248=14\frac{12}{48} = \frac{1}{4}
  • 312=14\frac{3}{12} = \frac{1}{4}

Each division yields the same factor: 14\frac{1}{4}.

This indicates a consistent operation of dividing by 44 between the terms. Thus, the rule in the sequence is to divide the current term by 44 to obtain the next term.

Therefore, this sequence follows the rule of dividing each number by 44 to get the next number.

Thus, the correct choice that corresponds to this pattern is: Yes, multiply by 4. \text{Yes, multiply by 4.}

Answer

Yes, multiply by 4.