What is the recursive rule for the geometric sequence in #10, -80, 640, -5120#?

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Answer 1 · 2017-09-28T11:54:55

The recursive rule is #g(n) = 10# when #n=1 # and
#g(n) = g(n-1)* -8 # when # n > 1 #

The geometric sequence is # g(n) :10, -80 ,640 ,-5120....#

The recusive defination of #g(n) # is

#g(n) = 10# when #n=1 # and #g(n) = g(n-1)* -8 # when # n > 1 #

# :. g(1) = 10 #

# :. g(2) = g(1) * - 8= 10* -8= -80 # similarly

# :. g(3) = g(2) * - 8= -80*-8= 640 #

# :. g(4) = g(3) * - 8= 640 * -8 = -5120 #

The recursive rule is #g(n) = 10# when #n=1 # and

#g(n) = g(n-1)* -8 # when # n > 1 # [Ans]