What is the 10th term of the geometric sequence 3, 12, 48, …?

1 Answer
Nov 26, 2015

Answer:

The #10#th term is #786432#

Explanation:

A geometric sequence is a sequence of the form
#a, ar, ar^2, ar^3, ...#
where #a# is an initial value and #r# is a common factor between terms.

Looking at this, we can tell that the #n#th term will be of the form #ar^(n-1)# and so the #10#th term will be #ar^9#.

In the given sequence, we start at #3# and thus #a=3#.

To find #r# we need only divide a term by the term prior to it. So, for example, dividing the second term by the first gives us

#r = (ar)/a = 12/3 = 4#

Thus the #10#th term is #3*4^9 = 786432#