Question

The second and eighth terms of a geometric sequence are 3 and 192, respectively. find the first term, common ratio, and an explicit rule for the nth term.

Answer 1

To solve the question we proceed as follows:
The explicit formula for geometric series is given by:
nth=ar^(n-1)
where:
a=first term
n=number of terms
second term is:
3=ar(2-1)
3=ar
thus
a=3/r

also the 8th term will be:
192=ar^(8-1)
192=ar^7
substituting the value of a in the above we get:
192=(3/r)r^7
this will give us
64=r^6
thus
r=2
hence the value of a will be:
a=3/2=1.5