177k views
2 votes
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.

1 Answer

6 votes
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
User Myrtho
by
8.7k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories