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Brut [27]
3 years ago
11

What is the recursive formula for this geometric sequence? -3, -21, -147, -1029, ...

Mathematics
2 answers:
den301095 [7]3 years ago
4 0

a_{n+1} =7a_{n}.

If we know the term n^{th} and the common relation, r, of a geometric sequence, you can find the term (n+1)^{th} using the recursive formula a_{n+1} =a_{n}.r.

The first term of the geometric sequence is a₁ = -3.

The common relation we have to find the relationship between a term and the term that precedes it.

r=\frac{-21}{-3} = 7

The recursive formula is:

a_{1} =-3

a_{n+1} =7a_{n}

Simora [160]3 years ago
3 0

a_1=-3\\r=7\\a_n=a_{n-1}\cdot r\\\\ \boxed{a_n=7a_{n-1}}

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The value of a will be  a=-\frac{1}{2}

Step-by-step explanation:

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so the y = 0 points are (1,0) and (4,0).

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3 years ago
Find an equation of the parabola with focus (2, −3) and directrix y = 1.
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Answer:

Step-by-step explanation:

The correct option is option (C).

The required equation of the parabola is

Step-by-step explanation:

Formula:

The distance of a point (x₁,y₁) from a line ax+by+c=0 is

.

The distance between two points (x₁,y₁) and (x₂,y₂) is

Given that, the focus of the parabola is (2,3) and directrix y= - 1.

We know that, a parabola is the locus of points that equidistant from the directrix and the focus.

Let any point on the parabola be  P(x,y)  .

The distance of P from the directrix is

           

=y+1

The distance of the point P from the focus (2,3) is

According to the problem,

 

The required equation of the parabola is

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