How do you find the first five terms given #a_1=-6# and #a_(n+1)=a_n+3#?

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Answer 1 · 2016-11-02T09:41:09

First five terms are #{-6,-3,0,3,6}#

As #a_(n+1)=a_n+3# and #a_1=-6#

#a_2=a_(1+1)=a_1+3=-6+3=-3#

#a_3=a_(2+1)=a_2+3=-3+3=0#

#a_4=a_(3+1)=a_3+3=0+3=3#

#a_5=a_(4+1)=a_4+3=3+3=6#

Hence, first five terms are #{-6,-3,0,3,6}#

Answer 2 · 2016-11-02T09:47:38

The first five terms of the arithmetic progression are #-6,-3,0,+3,+6.#

#a_(n+1)=a_n+3.# [GIVEN].
#:.a_(n+1)-a_n=3.#

#:.#When, #n=1,#
#a_2-a_1=3.#
#:.a_2+6=3.#
#:.a_2=-3.#

#:.#Common Difference #(d)=a_2-a_1=(-3)-(-6)=+3.#

#:. a_1=-6,a_2=-3,a_3=0,a_4=+3,a_5=+6.#

Therefore, the first five terms of the arithmetic progression are #-6,-3,0,+3,+6.# (answer).