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2 years ago

Use the sequence {−1,171,875;−234,375;−46,875;−9375,…} to answer the question.

Mathematics

1 answer:

AveGali [126]2 years ago

6 0

Answer:

an = −1,171,875(1/5)^n-1

Step-by-step explanation:

The given sequence is geometric sequence since they have the same common ratio r. The nth term of a geometric sequence is expressed as;

an = ar^n-1

n is the number of terms

r is the common ratio

a is the first term

From the sequence;

a = −1,171,875

r = −234,375 /−1,171,875 = -46,875/−234,375 = 0.2

r = 1/5

Substitute the values in the formula;

an = −1,171,875(1/5)^n-1

Hence the required explicit formula is an = −1,171,875(1/5)^n-1

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Write 17,924 in expanded form

vesna_86 [32]

Answer:

10,000 + 7,000 + 900 + 20 + 4

Step-by-step explanation:

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2 years ago

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What is the equation of the line, in point-slope form, that passes through the points (-1, 7) and (-2, 3)?

myrzilka [38]

Answer:

Step-by-step explanation:

(3-7)/(-2+1)= -4/-1= 4

y - 7 = 4(x + 1)

y - 7 = 4x + 4

y = 4x + 11

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3 years ago

6. Complete the two-column proof.

olya-2409 [2.1K]

Answer:

Given: $\frac{x}{6} + 2 = 15$ ......[1]

To prove : x =78

Subtraction property states that you subtract the same number to both sides of an equation.

Subtract 2 from both sides of an equation [1];

$\frac{x}{6} + 2 - 2= 15 -2$

Simplify:

$\frac{x}{6} = 13$ ......[2]

Multiplication property states that you multiply the same number to both sides of an equation.

Multiply 6 to both sides of an equation [2];

$\frac{x}{6} \times 6 = 13 \times 6$

Simplify:

$x = 78$ proved!

Statement Reason

1. $\frac{x}{6} + 2 = 15$ Given

2. $\frac{x}{6} = 13$ Subtraction property of equality

3. $x = 78$ Multiplication property of equality

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2 years ago

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Anyone know the answer?

Zepler [3.9K]

If you look from the points at angle 73, to 42, to 131, to z, the shape makes a quadrilateral.
Since the total of the interior angles in a quadrilateral add up to 360 you make an equation:

360 = 131 + 73 + 42 + 7 + x
Re-arrange the equation to get the x alone, by subtracting:
360 - 131 - 73 - 42 = x
114 = x

So x = 114 degrees<span />

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2 years ago

Express the terms of the following sequence by giving a recursive formula.

emmasim [6.3K]

The recursive formula for given sequence is: $a_n = a_{n-1}-7$

And the terms will be expressed as:

$a_1 = 11\\a_2 = a_{2-1} - 7 \\a_2= a_1 - 7\\a_2 = 11- 7\\a_2 = 4\\a_3 = a_{3-1} - 7 \\a_3= a_2 - 7\\a_3 = 4 - 7\\a_3 = -3\\a_4 = a_{4-1} - 7 \\a_4= a_3 - 7\\ a_4= -3 - 7\\a_4 = -10\\a_5 = a_{5-1} - 7 \\a_5= a_4 - 7\\a_5 = -10 - 7\\a_5 = -17\\$

Step-by-step explanation:

First of all, we have to determine if the given sequence is arithmetic sequence or geometric. For that purpose, we calculate the common difference and common ratio

Given sequence is:

11,4,-3,-10,-17...

Here

$a_1 = 11\\a_2 = 4\\a_3 = -3\\So,\\d = a_2 - a_1 = 4-11 = -7\\d = a_3-a_2 = -3-4 = -7$

As the common difference is same, given sequence is an arithmetic sequence.

A recursive formula is a formula that is used to generate the next term of the sequence using the previous term and common difference

So, the recursive formula for an arithmetic sequence is given by:

$a_n = a_{n-1} +d\\Putting\ d = -7\\a_n = a_{n-1}-7$

Hence,

The recursive formula for given sequence is: $a_n = a_{n-1}-7$

And the terms will be expressed as:

Keywords: arithmetic sequence, common difference

Learn more about arithmetic sequence at:

#LearnwithBrainly

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3 years ago