Respuesta :
Answer: The correct option is (B) [tex]a_n=3n+9.[/tex]
Step-by-step explanation: We are given to select the equation that represents the nth term of the following sequence :
12, 15, 18, 21, . . .
We see that
the given sequence is an arithmetic one with first term a = 12 and common difference d given by
d = 15 - 12 = 18 - 15 = 21 - 18 = . . . =3.
We know that
the nth term of an arithmetic sequence with first term a and common difference d is given by
[tex]a_n=a+(n-1)d.[/tex]
Therefore, the nth term of the given sequence is
[tex]a_n=a+(n-1)d=12+(n-1)\times3=12+3n-3=3n+9.[/tex]
Thus, the required nth term of the given sequence is [tex]a_n=3n+9.[/tex]
Option (B) is CORRECT.
