Question

A recursive rule for a geometric sequence is a1=3;an=1/2(an−1)

What is an explicit rule for this sequence?

Answer 1

A recursive rule for a geometric sequence is a1=3;an=1/2(an−1)
explicit rule
an = (3)(1/2 )^n−1

Answer 2

Answer:The explicit rule for this sequence:

`a_n=a_1(r)^(n-1)=3((1)/(2))^(n-1)`

Explanation:

`a_1=3`

`a_n=(1)/(2)a_(n-1)`

Where
`a_n` = n'th term in a sequence

`a_2=(1)/(2)a_((2-1))=(1)/(2)a_1=(1)/(2)* 3=(3)/(2)`

The value 'r' is geometric mean is given as:

r = common ratio

`r=(a_2)/(a_1)=((3)/(2))/(3)=(1)/(2)`

The explicit rule for this sequence:

`a_n=a_1(r)^(n-1)=3((1)/(2))^(n-1)`