Question

Identify each of the sequences in exercises 22 and 23 as arithmetic or geometric. State a rule for obtaining each number from the preceding number. What is the 12th num- ber in each sequence? 15, 30, 60, 120

Answer 1

The sequence showed is a Geometric sequence and the 12th number is 30720

Explanation:

It's a geometric sequence because there's a ratio, which we can multiply for any number and we'll get the next.

In the case showed the ratio is 2, for example

15x2=30

30x2=60

...

Then we can apply the following formula to find the n number of the sequence:

`a_(n) =a_(1) r^(n-1)`

Where

an= number we want to find

a1= first number of the sequence

r=ratio

In this case we have a ratio=2 and we want to find the 12th number:

`a_(12) =15 (2)^(12-1)\\ a_(12) =15 (2)^(11)=30720\\`