Question

In a geometric sequence a8=64 and a10=0.25 whats the value of a9

Answer 1

Hello, This is fine easy.

We have to calculate the value of reason.

an = ak . R ^ ( n - k )

We have :

a10 = 0,25

And

a8 = 64

Then follow:

a10 = a8 . R ^ (10-8)

0,25 = 64 . R ^ 2

0,25 / 64 = R^2

As 0,25 = 1 / 4

1 /4 / 64 = R^2

1 / 4 / 64 = 1/4 × 1 / 64

= 1 / 256

Then,

1/256 = R^2

R^2 = 1 / 256

R = √(1 / 256 )

R = √1 / √256

R = 1 / 16

Then , a9 = ?

a9 = a8 . R ^(9 -8)

a9 = 64 . ( 1 / 16 ) ^1

a9 = 64 . 1 / 16

a9 = 64 / 16

a9 = 4


This is the answer to the your question.

I hope this has helped

Answer 2

The ninth term i.e
`a^9` is 4

Explanation:

Given in G.P i.e geometric sequence

`a^8=64\text{ and }a^(10)=0.25`

`\text{we have to find the value of }a^9`

The recursive formula for G.P is

`a^n=ar^(n-1)`

As
`a^8=64`

⇒
`a^8=ar^(8-1)`

`64=ar^7` → (1)

Also,
`a^(10)=0.25`

⇒
`a^(10)=ar^(10-1)`

`0.25=ar^9` → (2)

Solving 1 and 2

`(ar^9)/(ar^7)=(0.25)/(64)`

`r^2=(1)/(256)`

`r=(1)/(16)`

Now,
`a^9=ar^(9-1)=ar^8=ar^7.r=64* (1)/(16)=4`

Hence, the ninth term is 4