Write an nth term rule for 6,−30,150,−750,... and find a_6

Noe Cowan

Noe Cowan

Answered question

2022-11-03

Write an nth term rule for 6,−30,150,−750,... and find a 6

Answer & Explanation

Gwendolyn Alexander

Gwendolyn Alexander

Beginner2022-11-04Added 16 answers

Let a n be the n t h 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

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