How do you write a rule for the nth term of the geometric sequence given the two terms a_3=5, a_6=5000?

1 Answer
Mar 19, 2017

Rule for the n^(th) term of the geometric sequence is a_n=10^(n-1)/20

Explanation:

If m^(th) term of a geometric sequence is a_m and n^(th) term of the sequence is a_n, then the common ratio r is given by

r=(a_n/a_m)^(1/((n-m)))

Here, we have a_3=5 and a_6=5000, hence

r=(5000/5)^(1/((6-3)))=1000^(1/(3))=root(3)1000=10

and as n^(th) term of a geometric sequence is given by

a_n=a_1xxr^(n-1) and hence as a_3=5

a_1=a_n/r^(n-1)=5/10^2=0.05

and rule for the n^(th) term of the geometric sequence is

a_n=0.05xx10^(n-1)=10^(n-1)/20