Question

A group of students is arranging squares into layers to create a project. The first layer has 6 squares. The second layer has 12 squares. Which formula represents an arithmetic explicit formula to determine the number of squares in each layer?
a1 = 6; an = 6 + an − 1, n > 0



a1 = 6; an = 6 ⋅ an − 1, n > 0



a1 = 6; an = 6 ⋅ an + 1, n > 0



a1 = 6; an = 6 + an + 1, n > 0

Answer 1

Answer:

Option 1.

Explicit formula : $a_n=6n$

Recursive formula : $a_n=a_{n-1}+6$

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.

$a_1=6$

$a_2=12$

It represents an arithmetic sequence 6, 12, 18, ....

Common difference is

$d=a_2-a_1=12-6$

The explicit formula of an AP is

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

where, a is first term and d is common difference.

Substitute a=6 and d=6 to find the explicit formula for given situation.

$a_n=6+(n-1)6$

$a_n=6+6n-6$

$a_n=6n$

The recursive formula of an AP is

$a_n=a_{n-1}+d$

Substitute d=6 to find the recursive formula for given situation.

$a_n=a_{n-1}+6$

where, n>0.

Therefore, the correct option is 1.

Answer 2

Answer:

$a_n=6n$

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:

$a_n=a_1+d(n-1)$

In this case your first term is:

$a_1=6$

and your difference is

$d=6$

substituting these values we have that

$a_{n}=6+6(n-1) \\a_n=6+6n-6\\a_n=6n$