Answer:
see explanation
Step-by-step explanation:
(11)
Note the differences in the values of the sequence
5 - 2 = 3
8 - 5 = 3
11 - 8 = 3
Since the differences are common then these are the terms of an arithmetic sequence with explicit formula
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference, thus
[tex]a_{n}[/tex] = 2 + 3(n - 1) = 2 + 3n - 3 = 3n - 1 ← explicit formula
(12)
A recursive formula allows the next term in the sequence to be found from the previous term.
To obtain the next term add 3 to the previous term, thus
[tex]a_{n+1}[/tex] = [tex]a_{n}[/tex] + 3 , with a₁ = 2
(13)
Using the explicit formula, then
[tex]a_{20}[/tex] = (3 × 20) - 1 = 60 - 1 = 59
