How do you find the first five terms of the sequence #a_1=7#, #a_(n+1)=a_n-2#?

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Answer 1 · 2017-09-18T00:42:16

# { 7, 5, 3, 1, -1 } #

We have:

# { (a_1,=7), (a_(n+1),=a_n-2) :} #

Put #n=1#

# a_2 = a_1 - 2 #
# \ \ \ \ = 7 - 2 #
# \ \ \ \ = 5 #

Put #n=2#

# a_3 = a_2 - 2 #
# \ \ \ \ = 5 - 2 #
# \ \ \ \ = 3 #

Put #n=3#

# a_4 = a_3 - 2 #
# \ \ \ \ = 3 - 2 #
# \ \ \ \ = 1 #

Put #n=4#

# a_5 = a_4 - 2 #
# \ \ \ \ = 1 #
# \ \ \ \ = -1 #

Hence, the first five terms of the sequence are:

# { a_1, a_2, a_3, a_4, a_5 } = { 7, 5, 3, 1, -1 } #