Answer:
a. geometric sequence
b. a<em>n</em> = 5(2)^n-1
c. a<em>n+1 </em>= a<em>n</em> x 2
Step-by-step explanation:
The sequence: 5, 10, 20, 40,...
a. The sequence is geometric because the sequence has a common ratio of 2, each number is made by multiplying the previous number with the common ratio (2).
b. The explicit formula for this sequence is a<em>n </em>= 5(2)^n-1
The explicit formula for a geometric sequence is
a<em>n</em> = a<em>1</em> (r)^n-1
Substituting that with the values we know, we will get
a<em>n</em> = 5(2)^n-1
c. The recursive formula for this sequence is a<em>n+1 </em>= a<em>n</em> x 2
The recursive formula for a geometric sequence is
a<em>n+1 </em>= a<em>n</em> x r
Substituting for the values we know, we get
a<em>n+1 </em>= a<em>n</em> x 2
Let me know in the comments if you have any questions! If you could mark this answer as brainliest, I would very much appreciate it
