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]
