Write the first four terms of each geometric sequence?

a. #a_1=5# and #r=2#
b. #a_1=6# and #r=1/2#

1 Answer
Apr 14, 2018

The first one: #5, 10, 20, 40#
The second one: #6, 3, 1.5, 0.75#

Explanation:

First, let's write the geometric sequences in an equation where we can plug them in:

#a_n=a_1*r^(n-1) rarr a_1# is the first term, #r# is the common ratio, #n# is the term you are trying to find (ex. the fourth term)

The first one is #a_n=5*2^(n-1)#. The second one is #a_n=6*(1/2)^(n-1)#.

First one:

We already know that the first term is #5#. Let's plug in #2, 3,# and #4# to find the next three terms.

#a_2=5*2^(2-1)=5*2^1=5*2=10#

#a_3=5*2^(3-1)=5*2^2=5*4=20#

#a_4=5*2^(4-1)=5*2^3=5*8=40#

Second one:

#a_2=6*(1/2)^(2-1)=6*(1/2)^1=6*1/2=3#

#a_3=6*(1/2)^(3-1)=6*(1/2)^2=6*1/4=1.5#

#a_4=6*(1/2)^(4-1)=6*(1/2)^3=6*1/8=0.75#

You could also simply multiply the first term (#a_1#) by the common ratio (#r#) to get the second term (#a_2#).

#a_n=a_(n-1)*r rarr# The previous term multiplied by the common ratio equals the next term.

The first one with a first term of #5# and a common ratio of #2#:

#5*2=10#

#10*2=20#

#20*2=40#

The second one with a first term of #6# and a common ratio of #1/2#:

#6*1/2=3#

#3*1/2=1.5#

#1.5*1/2=0.75#