How do you write an nth term rule for #6,-30,150,-750,...# and find #a_6#?

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Answer 1 · 2016-09-30T19:34:01

The n^(th) term #a_n" is "6(-5)^(n-1), and, a_6=-18750##.

Let #a_n# be the #n^(th)# term of the seq.

We observe that,

#a_2/a_1=a_3/a_2=a_4/a_3=...=-5#

So, if this pattern continue, we can say that the seq. is a Geom. Seq.,

having the First Term #a_1=6,# and, the Common Ratio #r=-5.#

For such a seq., #a_n=a_1*r^(n-1)=6(-5)^(n-1)#.

#:. a_6=6(-5)^5=-18750#