Question

Find the
13th term of the sequence
12, 21, 30,..
​

Answer 1

Answer:

What is the next number of the sequence 3, 12, 21, _, _, _?

The pattern from what is given looks to be that

3, 12, 21, _, _, _ is  

3, 3+9, 12+9, _, _, _  

⟹3, 3+9, 3+18, _, _, _  

⟹3+9×0, 3+9×1,  

3+9×2, _, _, _.  

So, continued on indefinitely, the  nth–––  number of the given sequence is  3+9n.  

So the 4th number is obtained by letting  n=4  in the formula:

3+4×9=3+36=39.  

Filling in the next two blanks shown in the question, get

3+5×9=3+45=48 and 3+6×9=3+54=57.

Answer 2

Answer:

Let a be the first term and d be the common difference

given AP : 12,21,30

a= 12

d= 9

Now,

A13= 12+(13-1)9

= 12+108

= 120

therefore the 13th term is 120