How do you find the first five terms of each sequence #a_1=0#, #a_(n+1)=-2a_n-4#?

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Answer 1 · 2017-07-02T22:03:10

# {0,4,-12,20,-44} #

We have a sequence:

# {a_n} = {a_1, a_2, a_3, ... } #

Where:

#\ \ \ \ a_1 =0#
#a_(n+1) = -2a_n-4#

Put #n=1 => a_2 = -2a_1 - 4#
# :. a_2 = -2(0) -4 #
# " " = 0-4 #
# " " = 4 #

Put #n=2 => a_3 = -2a_2 - 4#
# :. a_3 = -2(4) - 4 #
# " " = -8-4 #
# " " = -12 #

Put #n=3 => a_4 = -2a_3 - 4#
# :. a_4 = -2(-12) - 4 #
# " " = 24-4 #
# " " = 20 #

Put #n=4 => a_5 = -2a_4 - 4#
# :. a_5 = -2(20) - 4 #
# " " = -40-4 #
# " " = -44 #

Thus the first five terms #{a_1, a_2, a_3, a_5}# of the sequence #{a_n}# are:

# {0,4,-12,20,-44} #