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1 year ago

15. Which rule was used to create the arithmetic sequence below?

Mathematics

1 answer:

Nikolay [14]1 year ago

4 0

The rule used to create the arithmetic sequence -2, -4, -6, -8,.. is an = -2 - 2(n-1)

The arithmetic sequence is

-2, -4, -6, -8,...

The initial term = -2

The common difference = The second term - The first term

= -4 - (-2)

= -4 + 2

= -2

The nth term of the arithmetic sequence is

an = a+ (n-1) d

Where a is the initial term

an is the nth term

d is the common difference

Substitute the values in the equation

an = -2 + (n-1)(-2)

Rearrange the terms

an = -2 -2(n-1)

Hence, the rule used to create the arithmetic sequence -2, -4, -6, -8,.. is an = -2 - 2(n-1)

Learn more about arithmetic sequence here

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Answer:

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Step-by-step explanation:

we are given

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now, we can simplify

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$\frac{3(sin(a)+cos(a))-4(sin^3(a)+cos^3(a))}{sin(a)+cos(a)}$

now, we can factor it

$\frac{3(sin(a)+cos(a))-4(sin(a)+cos(a))(sin^2(a)+cos^2(a)-sin(a)cos(a)}{sin(a)+cos(a)}$

$\frac{(sin(a)+cos(a))[3-4(sin^2(a)+cos^2(a)-sin(a)cos(a)]}{sin(a)+cos(a)}$

we can use trig identity

$sin^2(a)+cos^2(a)=1$

$\frac{(sin(a)+cos(a))[3-4(1-sin(a)cos(a)]}{sin(a)+cos(a)}$

we can cancel terms

$=3-4(1-sin(a)cos(a))$

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$2sin(a)cos(a)=sin(2a)$

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Read 2 more answers

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Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

Given data

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