8|6|?|13|?|21|

Answer 1

To find the missing numbers in the sequence \(8, 6, ?, 13, ?, 21\), let's look for a pattern.

1. The first differences between consecutive numbers can help identify a pattern:
   • \(6 - 8 = -2\) (First difference between 8 and 6)
   • \(? - 6 = ?\) (We don't know this yet)
   • \(13 - ? = ?\) (We don't know this yet)
   • \(? - 13 = ?\) (We don't know this yet)
   • \(21 - ? = ?\) (We don't know this yet)

So, let's examine the existing numbers:

• From \(8\) to \(6\), we have a decrease of \(2\).
• From \(6\) to the next number (let's call it \(x\)):
  • If we follow a pattern, we could check if we have consistent increases or decreases.

Continuing with the pattern:

• If we assume an alternating addition/subtraction pattern:
  • From \(6\) to \(x\) could be a decrease.
  • From \(x\) to \(13\) could then be an increase.

If we assume that there are consistent increments in the pattern:

• We can assume that the first difference decreases by \(2\), and then the third number must be \(x - 3\).

Let's set up the equations assuming the missing numbers follow a consistent pattern:

1. \(x = 6 - d\)
2. \(13 = x + k\) (where \(k\) is an increment)

Starting from \(6\):

• If we take a step of \(-2\), then \(x\) must be \(8 - 2 = 6\) (confirming what we saw).

Now let's find the next number after \(13\):

• The pattern could hence be:
  • From \(x\) to \(13\) is an increase of \(7\) (from \(6\) to \(13\)).

Using our established pattern, if \(21 - 13 = 8\), this seems to continue a consistent line of additions of increasing integers.

If we summarize:

• \(8 - 2 = 6\)
• \(6 + 7 = 13\) (next number)
• \(13 + 8 = 21\) (next number)

Thus the missing values are:

• The first missing number is \(9\) (which fits: \(6 + 3\)).
• The second is \(17\) (which fits: \(13 + 4\)).

So the complete sequence is: 8, 6, 9, 13, 17, 21.