Answer:
[tex]a_{n}=2+3(n-1)[/tex]
Step-by-step explanation:
Step 1. To find the equation that describes the pattern, we use the arithmetic sequence formula:
[tex]a_{n}=a_{1}+d(n-1)[/tex]
Where a_n is the n'th terms and d is the common ratio between the numbers.
Step 2. The sequence we have is:
2 5 8 11
The first term is:
[tex]a_{1}=2[/tex]
And the common ratio or the difference between consecutive numbers is:
3 2+3=8 5+3=8 8+3=11
This will be the value of d:
d=3
Step 3. Substituting a_1 and d into the formula:
[tex]a_{n} =a_{1}+d(n-1)\\a_{n}=2+3(n-1)[/tex]
This is the equation that represents the number pattern, it represents that we add three each time to the previous number in the sequence.
Hence, the correct answer is [tex]a_{n}=2+3(n-1)[/tex]
