Question

given the recursive formula for a geometric sequence find the common ratio the 8th term and the explicit formula.did I set these up right

Answer 1

Answer:

Step-by-step explanation:

1)Since we know that recursive formula of the geometric sequence is

$a_{n}=a_{n-1}*r$

so comparing it with the given recursive formula $a_{n}=a_{n-1}*-4$

we get common ratio =-4

8th term= $a_{1}*(r)^{n-1}=-2*(-4)^{7} =32768.$

Explicit Formula =$-2*(-4)^{n-1}$

2) Comparing the given recursive formula $a_{n}=a_{n-1}*-2$

with standard recursive formula $a_{n}=a_{n-1}*r$

we get common ratio =-2

8th term= $a_{1}*(r)^{n-1}=-4*(-2)^{7} =512.$

Explicit Formula =$-4*(-2)^{n-1}$

3)Comparing the given recursive formula $a_{n}=a_{n-1}*3$

with standard recursive formula $a_{n}=a_{n-1}*r$

we get common ratio =3

8th term= $a_{1}*(r)^{n-1}=-1*(3)^{7} =-2187.$

Explicit Formula =$-1*(3)^{n-1}$

4)Comparing the given recursive formula $a_{n}=a_{n-1}*-4$

with standard recursive formula $a_{n}=a_{n-1}*r$

we get common ratio =-4

8th term= $a_{1}*(r)^{n-1}=3*(-4)^{7} =-49152.$

Explicit Formula =$3*(-4)^{n-1}$

5)Comparing the given recursive formula $a_{n}=a_{n-1}*-4$

with standard recursive formula $a_{n}=a_{n-1}*r$

we get common ratio =-4

8th term= $a_{1}*(r)^{n-1}=-4*(-4)^{7} =65536.$

Explicit Formula =$-4*(-4)^{n-1}$

6)Comparing the given recursive formula $a_{n}=a_{n-1}*-2$

with standard recursive formula $a_{n}=a_{n-1}*r$

we get common ratio =-2

8th term= $a_{1}*(r)^{n-1}=3*(-2)^{7} =-384.$

Explicit Formula =$3*(-2)^{n-1}$

7)Comparing the given recursive formula $a_{n}=a_{n-1}*-5$

with standard recursive formula $a_{n}=a_{n-1}*r$

we get common ratio =-5

8th term= $a_{1}*(r)^{n-1}=4*(-5)^{7} =-312500.$

Explicit Formula =$4*(-5)^{n-1}$

8)Comparing the given recursive formula $a_{n}=a_{n-1}*-5$

with standard recursive formula $a_{n}=a_{n-1}*r$

we get common ratio =-5

8th term= $a_{1}*(r)^{n-1}=2*(-5)^{7} =-156250.$

Explicit Formula =$2*(-5)^{n-1}$