Question

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

1.) Is the sequence arithmetic or geometric. Explain your answer.

2.) write the recursive rule for the sequence. Show your work

3.) write the explicit rule for this sequence

Answer 1

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