How do you write a rule for the nth term of the geometric term and then find #a_6# given #r=-1/2, a_3=8#?

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Answer 1 · 2017-06-14T10:52:03

#a_n=a_1*r^(n-1) and a_6= -1#

Rule of finding n th term of G.P is #a_n=a_1*r^(n-1)# .where #a_1,r,n#
are 1st term, common ratio and required term respectively.

#a_3=8 , r=-1/2, a_6= ?#

#a_3= a_1* (-1/2)^(3-1) or 8= a_1* (-1/2)^2 or 8 = a_1*1/4# or

#a_1=32 ; :. a_6= a_1* (-1/2)^(6-1) or a_6 = 32* (-1/2)^5# or

#a_6 = 32* (-1/32) = -1#

#a_6= -1 # [Ans]

Answer 2 · 2017-06-14T11:01:43

# a_n=32(-1/2)^(n-1), and, a_6=-1.#

In the Usual Notation for Geometric Sequence,

we are given, #r=-1/2, and, a_3=8....(1).#

Knowing that, #a_n=a_1*r^(n-1)," we have, using "(1),#

#8=a_3=a_1*(-1/2)^(3-1), or, a_1=32.#

#:. a_n=32(-1/2)^(n-1).#

#:. a_6=32(-1/2)^5=-1.#