A geometric sequence has common ratio 4. The second term is 9 more than the first term. What is the first term?

1 Answer
Aug 27, 2017

The first term is #3#.

Explanation:

The nth term of a geometric sequence is given by #t_n = a(r)^(n - 1)#. Thus,

#t_1 = ar^0 = a#
#t_2 = a + 9#

It's given that the common ratio is #4#, hence:

#t_2 = (a)4^1 -> t_2 = 4a #

We now have a system of equations. If we substitute the second equation into the first, we get:

#4a = a + 9#

#3a = 9#

#a = 3#

Let's check our answer. If #t_1 = 3#, and the common ratio is #4#, then #t_2 = 12#. Since #12 - 3 = 9#, this means the second term indeed is #9# more than the first, confirming that our answer is correct.

Hopefully this helps!