Question

Hi, I'm actually a good student i do my own work but this stuff makes no sense to me, my teacher isn't the best so if you could provide a answer and IF possible a explanation for each problem on how you got it, it would be great. also kind of needed asap. thank you.
1. enter the explicit rule for the geometric sequence
15,3,3/5,3/25,...

an= _

2. enter a recursive rule for the geometric sequence
10,-80,640,-5120,...

a1=_; an=_

3. the reursive rule for the a geometric sequence is given
a1= 2; an= 1/3 an-1

enter the explicit rule for the sequence

an=_

4. the explicit rule for the sequence is given
an= 1/2(4/3)n-1

enter the recursive rule for the geometric sequence
a1=_; an=_

Answer 1

1. an = 15 (1/3)^(n-1)
because it starts from 1,2,3,4........ for n.
2. a₁= 10(-8)^(1-1)=10
an= 10(-8)^(n-1)
3. an=2(1/3)^(n-1)
4. a₁= 1/2 (4/3)^0=1/2
an= 1/2 (4/3)^(n-1)
Hopes this loves.