Answer :

Answer:

[tex]a_{n}[/tex] = 3n - 1

Step-by-step explanation:

Note there is a common difference d between consecutive terms in the sequence, that is

5 - 2 = 8 - 5 = 11 - 8 = 14 - 11 = 3

This indicates the sequence is arithmetic with n th term

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 2 and d = 3, thus

[tex]a_{n}[/tex] = 2 + 3(n - 1) = 2 + 3n - 3 = 3n - 1

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