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Predict the next three numbers in the pattern.

[tex]\[ 2, 3, 5, 8, 13, 21 \][/tex] [tex]\(\square\)[/tex] [tex]\(\square\)[/tex] [tex]\(\square\)[/tex]

Sagot :

GinnyAnsweridn
To determine the next three numbers in the given sequence [tex]\(2, 3, 5, 8, 13, 21\)[/tex], observe the pattern used to generate it.

Let's analyze how the sequence progresses from one term to the next:
- The 1st term is 2.
- The 2nd term is 3.
- The 3rd term is 5.
- The 4th term is 8.
- The 5th term is 13.
- The 6th term is 21.

Notice that each term after the first two is obtained by adding the two preceding terms.

1. To find the 7th term:
- Add the 5th term (13) and the 6th term (21).
[tex]\[ 13 + 21 = 34 \][/tex]
So, the 7th term is 34.

2. To find the 8th term:
- Add the 6th term (21) and the 7th term (34).
[tex]\[ 21 + 34 = 55 \][/tex]
So, the 8th term is 55.

3. To find the 9th term:
- Add the 7th term (34) and the 8th term (55).
[tex]\[ 34 + 55 = 89 \][/tex]
So, the 9th term is 89.

Therefore, the next three numbers in the pattern are:
[tex]\[ 34, 55, \text{and} 89 \][/tex]
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