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3 years ago

2,-10,50,-250,.. Geometric sequence

Mathematics

1 answer:

nikklg [1K]3 years ago

8 0

This question is incomplete, here is the complete question

What is the recursive formula for this geometric sequence 2, -10, 50, -250, .... ?

The recursive formula for this geometric sequence is:

$a_{1}$ = 2; $a_{n}$ = (-5) • $a_{n-1}$

Step-by-step explanation:

To find the recursive formula for a geometric sequence:

Determine if the sequence is geometric (Do you multiply, or divide, the same amount from one term to the next?)
Find the common ratio. (The number you multiply or divide.)
Create a recursive formula by stating the first term, and then stating the formula to be the common ratio times the previous term.

The recursive formula is:

$a_{1}$ = first term; $a_{n}$ = r • $a_{n-1}$ , where

$a_{1}$ is the first term in the sequence
$a_{n-1}$ is the term before the nth term
r is the common ratio

∵ The geometric sequence is 2 , -10 , 50 , -250

∴ $a_{1}$ = 2

- To find r divide the 2nd term by the first term

∵ $r=\frac{a_{2}}{a_{1}}$

∴ $r=\frac{-10}{2}=-5$

- Substitute the values of $a_{1}$ and r in the formula above

∴ $a_{1}$ = 2; $a_{n}$ = (-5) • $a_{n-1}$

The recursive formula for this geometric sequence is:

$a_{1}$ = 2; $a_{n}$ = (-5) • $a_{n-1}$

Learn more:

You can learn more about the geometric sequence in brainly.com/question/1522572

#LearnwithBrainly

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(m? - 5 m +6 )<br>÷(m - 2)

leonid [27]

Answer:

(m? - 5 m +6 ) ÷ (m - 2) = $\frac{m}{-5m+6} / (m - 2)$

Step-by-step explanation:

Divide the first expression by the second expression.

$\frac{m}{-5m+6} / (m - 2)$

I hope this helps.

4 0

3 years ago

Read 2 more answers

Suppose that the water level of a river is 34 feet and that it is receding at a rate of her foot per day right in equation and h

Ghella [55]

Answer: it will take 9 days

Step-by-step explanation:

The water level was initially at 34feet it was receding at the rate of a foot per day. The rate at which it was receding is linear, thus, it is in an arithmetic progression. The formula for the nth term of an arithmetic progression is expressed as

Tn = a+(n-1)d

Where

a is the first term if the sequence

d is the common difference

n is the number of terms.

From the information given,

a = 34 feet because it is the initial height

n is the number of days it will take to get to 26 ft

d = -1 because it is decreasing by 1 foot per day.

Tn = T26 = 26 feet. Therefore, the equation will be

Tn = 34 -1(n-1)

To find for T26,

26= 34 + (n - 1)-1

26 - 34 = -n + 1

n - 1 = 8

n = 8 + 1 = 9

8 0

3 years ago

Hello! Can someone please help me with this question ? I’ll mark brainly thanks ! :)

NikAS [45]

Answer:

$\Large\boxed{\text{Perpendicular Equation:} \ y = -\frac{2}{7}x + \frac{22}{7}}$

$\Large\boxed{\text{Parallel Equation:} \ y = \frac{7}{2}x -12}$

Step-by-step explanation:

In order to find the equations that are parallel/perpendicular to the line $y = \frac{7}{2}x - 4$ , we need to note a couple things about the relationships between lines and their parallel/perpendicular lines.

A) If a line is perpendicular to another, the slopes will be opposite reciprocals (for instance $-2$ and $\frac{1}{2}$ - multiplied, they equal -1.)
B) If a line is parallel to another, they will have the exact same slope.

<h2>Perpendicular:</h2>

We know that the slope of a perpendicular line will be the the opposite reciprocal of the line we're comparing it to.

Since the slope of our base line is $\frac{7}{2}$ , we can find the reciprocal, then the opposite of that.

Reciprocal of $\frac{7}{2} = \frac{2}{7}$
Opposite of $\frac{2}{7} = -\frac{2}{7}$

So the slope of this line will be $-\frac{2}{7}$ , making our equation $y = -\frac{2}{7}x+ b$

However, y-intercepts will not stay the same. In order to find this, we can substitute the point (4, 2) into our equation to solve for b.

$2 = -\frac{2}{7} \cdot 4 + b$
$2 = -\frac{8}{7} + b$
$b = 2+\frac{8}{7}$
$b = 2 \frac{8}{7}$
$b=\frac{22}{7}$

Now we know the y-intercept of this equation is $\frac{22}{7}$ . We can now finish off our equation of the line by substituting that in to what we already have, $y = -\frac{2}{7}x+ b$ .

$y = -\frac{2}{7}x+ \frac{22}{7}$

<h2>Parallel:</h2>

As mentioned earlier, parallel lines will have the exact same slope but not the same y-intercept. Since the slope of our original equation is $\frac{7}{2}$ , the slope for this one will also be $\frac{7}{2}$ .

So we now know the equation looks something like $y = \frac{7}{2}x + b$ .