Verified Answer :

David1993

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:

The ninth term i.e \(a^9\)  is 4

Step-by-step 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

\(\frac{ar^9}{ar^7}=\frac{0.25}{64}\)

\(r^2=\frac{1}{256}\)

\(r=\frac{1}{16}\)

Now, \(a^9=ar^{9-1}=ar^8=ar^7.r=64\times \frac{1}{16}=4\)

Hence, the ninth term is 4

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