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bagirrra123 [75]
3 years ago
11

What is the common ratio and explicit formula for -2,6,-18,54?

Mathematics
1 answer:
Snezhnost [94]3 years ago
6 0

Answer:

The explicit formula for a given geometric sequence is of the form

a_{4} =\frac{1}{(a_{1})^4}

Step-by-step explanation:

Given sequence is {\{-2,6,-18,54}\}

Let a_{1}=-2,a_{2}=6,a_{3}=-18,a_{4}=54

To find the common ratio r:

r=\frac{a_{2}}{a_{1}}

=\frac{6}{-2}

=-3

Therefore r=-3

r=\frac{a_{3}}{a_{2}}

=\frac{-18}{6}

=-3

Therefore r=-3

Therefore common ratio is -3

Therefore given sequence is geometric sequence.

The explicit formula for a geometric sequence is a_{n}=a_{1}^{r-1}, where common ratio is r.

From given sequence we are having  r=-3

Therefore the explicit formula for a given geometric sequence is of the form a_{4} =a_{1}^{-3-1}

a_{4} =a_{1}^{-4}

a_{4} =\frac{1}{(a_{1})^4}

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