How do you write a rule for the nth term of the geometric term given the two terms #a_2=2, a_5=1/4#?

1 Answer
May 22, 2017

Answer:

#a_n=4*(1/2)^(n-1)#

Explanation:

The general form for a geometric sequence is:
#a_n=a_1*r^(n-1)#

With this, you can write a system of equations:
#a_2=a_1*r^(2-1)#
#a_5=a_1*r^(5-1)#

#2=a_1*r^1#
#0.25=a_1*r^4#
#r^4/r^1=0.25/2#
#r^3=0.125#
#r=0.5#

Now, find the first term.
#a_2=a_1*0.5^1#
#2=a_1*0.5#
#a_1=4#

Using the formula stated above, we get:
#a_n=4*0.5^(n-1)#