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., $a_n=a_1*r^(n-1)=6(-5)^(n-1)$ .

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

How do you write an nth term rule for 6,-30,150,-750,...6,-30,150,-750,... and find a_6a_6?