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.

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