# the first term of geometric sequence is 24 and the third term is 6, find the fourth term and expression for the nth term.?

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• The first term of geometric sequence is 24 and the third term is 6.

The fourth term is 3.

24, 12, 6, 3, ...

The expression for the n th term:

an = 3 × 2^(4 - n)

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• a = 24 , a r² = 6

r² = 6/24 = 1/4

r = 1/2

Terms are 24 , 12 , 6 , 3

Un = 24 x (1/2)^(n - 1)

Un = 48 / 2^n

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• 24k^2 = 6

k = { -1/2 , 1/2}

Fourth term = { 3 , -3 }

X_n = 48(.5)^n ; 48(-.5)^n

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• 24, 12, 6, 3, ..., 48/(2)ⁿ, ...

or

24, -12, 6, -3, ..., -48/(-2)ⁿ, ...

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• You Are given: 24, 24r, 24r², 24r^3, ... You are then told that 24r² = 6. So what is r?

So what is then 24r^3?

Then 24rⁿ?

Done!

Hopefully no one will spoil you the answer thereby depriving you from your personal enhancement; that would be very inconsiderate of them.

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• t_n = t(n-1) * r

so

t_1 = 24

t_2 = 24 * r

t_3 = 24*r^2 = 6

==> r^2 = 6/24 = 1/4

==> r = 1/2

so t_4 = 3

and t_n = 24*2^(-n)

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