Question

The sequence 2,6,18,54 shows the number of sit-ups Alan can do each day.

Answer 1

Step-by-step explanation:

this sequence is geometric not arithmetic

HOw we know that ??

when we get a common difference  that must Be equal  

d=6-2=4  not equal to  d=18-6=12

So it is not arithmetic

but when we get the common ratio that also must be equal

r=6/2=18/6=54/18=3    equal

So it is geometric

By using this equation:

a(n)=a(1)*r^(n-1)

and we have a(1)=2 , r=3    

Explicit rule: a(n)=2*(3)^(n-1)

Recursive rule:  a(n)= r * a(n-1)

a(n-1) ⇒ priviuse term

SO:  a(n)= 3 * a(n-1)

For example:

a(3)= 3 * 6 =18

I really hope this helps <3