How do you find the 5th term of the sequence in which #t_1 = 8# and #t_n = -3t_n-1#?

1 Answer
Dec 16, 2015

Answer:

#t_5 = 648#

Explanation:

Given the sequence #t_1 = 8, t_n = -3t_(n-1)# we have

#t_1 = 8#

#t_2 = -3t_1 = -24#

#t_3 = -3t_2 = 72#

#t_4 = -3t_3 = -216#

#t_5 = -3t_4 = 648#

Note that in general, as every term after the first is just #-3# multiplied by the previous term, we can express the #n^(th)# term directly as

#t_n = (-3)^(n-1)t_1 = (-3)^(n-1)*8#

In general, a sequence of the form

#a, ar, ar^2, ar^3, ..., ar^n, ...#

is called a geometric sequence.