MATHEMATICS HIGH SCHOOL

Determine the common ratio and find the next three terms of the geometric sequence.-7, 3.5, -1.75 ...
a.
-0.5; 0.450, -0.8655, 0.45985
c.
-1.5; 0.450, -0.8655, 0.45985
b.
-0.5; 0.875, -0.4375, 0.21875
d.
-1.5; 0.875, -0.4375, 0.21875

Answers

Answer 1

Answer:

Answer:

$a_(4) =0.875$

$a_5=-0.4375$

$a_6=0.21875$

Step-by-step explanation:

As we know that a geometric sequence does have the common ratio whoch is defined as the ratio of a term to the preceding term.

This common ratio is normally denoted by the 'r'.

As the given sequence is

$-7, 3.5, -1.75 ...$

So,

$r=(3.5)/(-7)=-0.5, r=-(1.75)/(3.5)=-0.5$

To find the nth term of a geometric sequence we use the formula:

$a_(n) =a_(1) r^(n-1)$

where,

r is the common ratio and $a_(1)$ being the first term.

So, the next three terms i.e. $a_(4), a_(5)$ and $a_(6)$ can be obtained by substituting the values of n = 4, n = 5 and n = 6 respectively in $a_(n) =a_(1) r^(n-1)$ .

$a_(1) =-7$

$r=-0.5$

$a_(n) =a_(1) r^(n-1)$

So, $a_(4), a_(5)$ and $a_(6)$ can be obtained by substituting the values of n = 4, n = 5 and n = 6 respectively in $a_(n) =a_(1) r^(n-1)$ when $a_(1) =-7$ and $r=-0.5$ .

$a_(4) =a_(1) r^(4-1)$

$a_(4) =(-7) r^(3)$

$a_(4) =(-7) (-0.5)^(3)$

$a_(4) =0.875$

$a_(5) =a_(1) r^(5-1)$

$a_(5) =(-7) r^(4)$

$a_(5) =(-7) (-0.5)^(4)$

$a_5=-0.4375$

$a_(6) =a_(1) r^(6-1)$

$a_(6) =(-7) r^(5)$

$a_(6) =(-7) (-0.5)^(5)$

$a_6=0.21875$

Therefore,

$a_(4) =0.875$

$a_5=-0.4375$

$a_6=0.21875$

Keywords: geometric sequence, common ratio

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the model an=395n +5419 describes the cost of tution and fees at public colleges in academic year n, where n=1 corresponds to the school year ending in 2007,n=2 to the school year ending in 2008 and so on four years

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Answers

Just substitute 4 in for n, then you would get 395*4 +5419. That is 6999, so it's 6999 for four years.

$\boxed{a_n=395n+5419}\n \n a_4=395*4+5419\n \n a_4=1580+5419\n \n \boxed{\boxed{a_4=6,999}}$

When a pair of blue jeans is made the leftover denim scraps can be recycled to make stationerypencils and more denim One pound of denim is left after making every five pairs of jeans. How
many pounds of denim would be left from 250 pairs of jeans

Answers

Answer:

50 pounds

Step-by-step explanation:

What must be added to
2x² - 3 xy + 5yz to get x² - xy + y²

Answers

Answer:

-x² + y² + 2xy - 5yz

Step-by-step explanation:

"A" must be added to first expression to get the second one:

A + 2x² - 3 xy + 5yz = x² - xy + y²
A = ?

------------------------

A = x² - xy + y² - (2x² - 3 xy + 5yz) =
x² - xy + y² - 2x² + 3 xy - 5yz=
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Please help me with these 6 through 10 :)

Answers

6.) constant = 75

7.) open sentence = 6 + 22 = 28

8.) equation = 17 + b = 47

9.) solution = when x + 37 = 62, x = 25

PLZ HELP ALGEBRA!!!!
AND PLZ SHOW WORK

Answers

Answer:

Step-by-step explanation:

n is the number of times the interest compounds per year. If the interest in this problem only compounds once per year ("annually"), then n = 1 and you'd be just as well off to use the formula:

$A=P(1+r)^t$

When n = 1, r/n is just r. But I'll show you using the formula they want you to use; it's the same anyways.

For us, P = 500, r = .015, n = 1. Filling that into the formula:

$A=500(1+(.015)/(1))^((1)(t))$ which simplifies down to

$A=500(1+.015)^t$ and

$A=500(1.015)^t$ (see what I meant about not having to use the formula with "n" in it if n 1?)

That formula is the answer to part a. For part b, we are to find how long it takes for the account to reach $800. $800 goes in for A:

$800=500(1.015)^t$

Begin by dividing both sides by 500 to get:

$1.6=(1.015)^t$

The only way to bring that t down from its current exponential position is to take the natural log of both sides. I will do that and at the same time apply the power rule for logs which says the exponent will come down out in front of the log:

$ln(1.6)=tln(1.015)$