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

71) a common ratio =-4, 8th term= 01 * (r)-1-2*(-4)7 = 32768, Explicit Formula =-2*(-4)-1

72) a common ratio =-2, 8th term=1 * (r)-1-4*(-2)7 = 512, Explicit Formula =-4* (-2)-1

73) a common ratio =3, 8th term=1 * (r)-1-1 (3)7 = -2187, Explicit Formula =-1 * (3)-1

74) a common ratio =-4, 8th term=a1 * (r)-1 = 3*(-4)7= -49152, Explicit Formula =3* (-4)2-1

75) a common ratio =-4, 8th term=1 * (r)-1-4*(-4) = 65536, Explicit Formula =-4*(-4)-1

76) a common ratio =-2, 8th term=a1 * (r)-13 (-2)7 = -384, Explicit Formula =3* (-2)-1

77) a common ratio =-5, 8th term= 01 * (r)-14*(-5)7=-312500, Explicit Formula =4* (-5)-1

78) a common ratio =-5, 8th term= 11 * (r)n-12*(-5)7-156250, Explicit Formula =2*(-5)-1

71) Since we know that the recursive formula of the geometric sequence is An-1*T

so comparing it with the given recursive formula anan-1-4

we get a common ratio =-4

8th term= 01 * (r)-1-2*(-4)7 = 32768.

Explicit Formula =-2*(-4)-1

72) Comparing the given recursive formula an an-1-2

with standard recursive formula an= An-1*T

we get a common ratio =-2

8th term=1 * (r)-1-4*(-2)7 = 512.

Explicit Formula =-4* (-2)-1

73) Comparing the given recursive formula An = An-1*3

with standard recursive formulation An-1*r

we get a common ratio =3

8th term=1 * (r)-1-1 (3)7 = -2187.

Explicit Formula =-1 * (3)-1

74) Comparing the given recursive formula = An-1-4

with standard recursive formula an An-1*r

we get a common ratio =-4

8th term=a1 * (r)-1 = 3*(-4)7= -49152.

Explicit Formula =3* (-4)2-1

75) Comparing the given recursive formula with a standard recursive formula an An-1*r An-1-4

we get a common ratio =-4

8th term=1 * (r)-1-4*(-4) = 65536.

Explicit Formula =-4*(-4)-1

76) Comparing the given recursive formula An = an-1-2 with standard recursive formula an= An-1* T

we get a common ratio =-2

8th term=a1 * (r)-13 (-2)7 = -384.

Explicit Formula =3* (-2)-1

77) Comparing the given recursive formula anan-1-5 with standard recursive formula un An-1 *r

we get a common ratio =-5

8th term= 01 * (r)-14*(-5)7=-312500.

Explicit Formula =4* (-5)-1

78) Comparing the given recursive formula An An-1-5

with standard recursive formulation An-1*r

we get a common ratio =-5

8th term= 11 * (r)n-12*(-5)7-156250.

Explicit Formula =2*(-5)-1

Answer 2

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)`