Answer:
[tex]a_n=6n[/tex]
Step-by-step explanation:
This is an example of an arithmetic sequence that is that the following term is obtained by adding or substracting a number called difference the formula for this sequence is:
[tex]a_n=a_1+d(n-1)[/tex]
In this case your first term is:
[tex]a_1=6[/tex]
and your difference is
[tex]d=6[/tex]
substituting these values we have that
[tex]a_{n}=6+6(n-1) \\a_n=6+6n-6\\a_n=6n[/tex]
Answer:
Option 1.
Explicit formula : [tex]a_n=6n[/tex]
Recursive formula : [tex]a_n=a_{n-1}+6[/tex]
Step-by-step explanation:
All options represent the recursive formulas.
It is given that the first layer has 6 squares. The second layer has 12 squares.
[tex]a_1=6[/tex]
[tex]a_2=12[/tex]
It represents an arithmetic sequence 6, 12, 18, ....
Common difference is
[tex]d=a_2-a_1=12-6[/tex]
The explicit formula of an AP is
[tex]a_n=a+(n-1)d[/tex]
where, a is first term and d is common difference.
Substitute a=6 and d=6 to find the explicit formula for given situation.
[tex]a_n=6+(n-1)6[/tex]
[tex]a_n=6+6n-6[/tex]
[tex]a_n=6n[/tex]
The recursive formula of an AP is
[tex]a_n=a_{n-1}+d[/tex]
Substitute d=6 to find the recursive formula for given situation.
[tex]a_n=a_{n-1}+6[/tex]
where, n>0.
Therefore, the correct option is 1.
