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Vikki [24]
3 years ago
11

Complete the recursive formula of the geometric sequence 27,−9,3,−1,

Mathematics
1 answer:
natita [175]3 years ago
5 0

Step-by-step explanation:

a1 = 27

r = -9/27 = -⅓

the formula :

an = a1. r^(n-1)

= 27. (-⅓)^(n-1)

= 3³(-3`¹)^(n-1)

= 3³(-3)^(1-n)

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Which formula can be used to find the nth term of a geometric sequence where the fifth term is 1/16 and the common ratio is 1/4?
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Any geometric sequence can be expressed as:

a(n)=ar^(n-1), a=initial term, r=common ratio, n=term number

We are given that a(5)=1/16 and r=1/4 so we can say:

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1/16=a(1/4)^4

1/16=a/256

256/16=a

16=a

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a(n)=16(1/4)^(n-1)


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