MATH SOLVE

3 months ago

Q:
# 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

Accepted Solution

A:

Answer:The sequence showed is a Geometric sequence and the 12th number is 30720Step-by-step 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 example15x2=3030x2=60...Then we can apply the following formula to find the n number of the sequence:[tex]a_{n} =a_{1} r^{n-1}[/tex]Wherean= number we want to finda1= first number of the sequencer=ratioIn this case we have a ratio=2 and we want to find the 12th number:[tex]a_{12} =15 (2)^{12-1}\\ a_{12} =15 (2)^{11}=30720\\[/tex]