Consider the given geometric sequence. 16, 32, 64, 128, ... 50 points!! Given that the sequence is represented by the function f, complete the statements. The common ratio is ..…

Question

asked Mar 1, 2020 106k views

2 Answers

Jayquan · Answer 1 · 2020-03-05T18:57:15+0000

Answer: The common ratio is 2.

f(1)=16

f(5)=256

Explanation:

The given geometric sequence. is

16, 32, 64, 128, ...

Also, The common ratio (r)=
(a_(n+1))/(a_n)=(a_2)/(a_1)=(32)/(16)=2

Hence, the common ratio (r)= 2

Given that the sequence is represented by the function f.

Then
f(n)=a_1r^(n-1)

Then, the first term of G.P. =
f(1)=16

For n=5,
f(5)=16(2)^(5-1)=16(2)^4=16*16=256

Hence, f(5)=256