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Which of the following represents the general equation for the geometric sequence? -1, -2, -4, ... an = 1 · 2n - 1 an = -2n - 1 an = 2n - 1 an = 1 · 2n + 1

User Fijjit
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2 Answers

4 votes
-1,-2,-4

an = a1 * r^(n - 1)
a1 = first term = -1
r = common ratio = 2

so the equation would be : an = -1 * 2^(n - 1)
User Antineutrino
by
7.5k points
3 votes

Answer:


a_(n) =  - 2^(n-1).

Explanation:

Given : geometric sequence -1, -2, -4, ...

To find : Which of the following represents the general equation for the geometric sequence.

Solution : We have given

Geometric sequence -1, -2, -4, ...

By the formula for general equation :
a_(n) = a_(1) *r^(n-1).

Where,
a_(n) = last term.


a_(1) = first term.

r = common ratio.

r ( common ratio ) =
(second\term)/(first\term).

In -1, -2, -4, ...


a_(1) = -1.

r ( common ratio ) =
(-2)/(-1).

r ( common ratio ) =2.

Plug the values in formula


a_(n) =  (-1) * 2^(n-1).


a_(n) =  - 2^(n-1).

Therefore,
a_(n) =  - 2^(n-1).

User Sergii Volchkov
by
8.2k points

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