# 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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- KrishnamurthyLv 71 month ago
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)

- ComoLv 71 month ago
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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- rotchmLv 71 month ago
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.

- L. E. GantLv 71 month ago
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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