find the formula for u sub n Assume the sequence is geometri

find the formula for u sub n. Assume the sequence is geometric.

u sub 2=192

u sub 7= 6

Solution

Let the geometric series whose first term is \'u\' and common ratio is \'r\'

then geometric sequence will be- u, ur, ur^2, ur^3, ur^4,    .............ur^n

Given u sub 2=192 (say 2nd term)

=> ur=192..............(1)

Also given, u sub 7=6 (say 7th term)

=> ur^6=6............(2)

now dividing euation (2) by equation (1)

(ur^6)/ur = r^5=6/192=1/32=(1/2)^5

=> r=1/2

now first term u=192/r=192/(1/2)= 384

Therfore formula ur^n=384(1/2)^(n-1)