For a glven geometric sequence, the 8^th term, a_(8) Is equal to (31)/(27) and the 12^th term, a_(12) Is equal to 93 Find the value of the 16^th term, a_(16) If applicat write your answer as a fraction. a_(16)=square

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Answer 1

To find the value of the 16th term,

, we can use the formula for the nth term of a geometric sequence:

where

is the nth term,

is the first term, and

is the common ratio.Given that the 8th term,

, is equal to

and the 12th term,

, is equal to 93, we can set up two equations:

We can solve these equations simultaneously to find the values of

and

.Dividing the second equation by the first equation, we get:

Substituting the given values, we have:

Simplifying the left side, we get:

Calculating the left side, we have:

Taking the fourth root of both sides, we get:

Substituting this value of

back into the first equation, we can solve for

:

Simplifying the left side, we have:

Dividing both sides by 2187, we get:

Simplifying the right side, we have:

Now that we have found the values of

and

, we can find the value of the 16th term,

:

Substituting the values of

and

, we have:

Simplifying the right side, we get:

Therefore, the value of the 16th term,

, is

.

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