Question

Which is an equation for the nth term of the sequence?

Answer 1

Answer:  The correct option is (B) $a_n=3n+9.$

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

$a_n=a+(n-1)d.$

Therefore, the nth term of the given sequence is

$a_n=a+(n-1)d=12+(n-1)\times3=12+3n-3=3n+9.$

Thus, the required nth term of the given sequence is $a_n=3n+9.$

Option (B) is CORRECT.

Answer 2

The answer is a I think