How do you find the next three terms in the geometric sequence -16, 4, , , ... ?

2 Answers
Nov 6, 2015

Answer:

Find the common ratio #r# between terms, and multiply by it repeatedly to obtain #-1, 1/4, -1/16# as the next three terms in the sequence.

Explanation:

The general form for a geometric sequence with the first term #a# is #a, ar, ar^2, ar^3, ...# where #r# is a common ratio between terms.

As the first two terms of the geometric sequence given are #-16# and #4#, we have #a = -16# and #ar = 4#.

Then, to find #r#, we simply divide the second term by the first to obtain
#(ar)/a = 4/(-16)#
#=> r = -1/4#

Thus the next three terms in the sequence will be
#ar^2 = 4*(-1/4) = -1#
#ar^3 = -1 * (-1/4) = 1/4#
#ar^4 = 1/4 * (-1/4) = -1/16#

Nov 6, 2015

Answer:

#(x_n)=-16, 4, -1, 1/4, -1/16, ...#

Explanation:

Since it is a geometric sequence #(x_n)#, there is a constant ratio #r=(x_(n+1)/x_n)=4/-16=-1/4#

So if #a=-16# is the first term #x_1#, then general term is given by #x_n=ar^(n-1)=-16*(-1/4)^(n-1)#

Hence the 3rd term, #x_3=-16*(-1/4)^(3-1)=-1#

Similarly #x_4=1/4 and x_5=-1/16#