Arecursive rule for a geometric sequence is a1=8; an=3/4an−1 . what is the explicit rule for this sequence?

The explicit rule for this sequence is;

Step-by-step explanation:

Given the statement: A recursive rule for a geometric sequence is

and

for n= 2;

Similarly for n = 3;

Therefore, we get a geometric sequence i.e,

Now, to find the explicit rule for this geometric sequence:

A geometric sequence states that  a sequence of numbers that follows a pattern were the next term is found by multiplying by a constant called the common ratio(r).

It is given by: where is the first term, r s the common ratio and n is the number of terms;

In the given sequence:  ,

then, the explicit rule for this sequence is;

answer

d. 10

explanation

the distance from point y to wx is the height of the triangle.

using pythagoras theorem,

group similar terms to get,

this implies that,

take positive square root of both sides to get,

this implies that,

step-by-step explanation:

we have

using a graphing tool

see the attached figure

this is a quadratic equation (vertical parabola) open up

the vertex is a > vertex

the domain of the function is all real > interval (-∞,∞)

the range of the function is the > [-6.125,∞)

the function has two x->   and

the function is increasing over the > (0.25,∞)

the function is decreasing over the > (-∞,0.25)