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3 years ago

Write a formula that will yield the nth term of the sequence: 3,-2,-7,-12

Mathematics

1 answer:

RUDIKE [14]3 years ago

8 0

Answer:

-5n + 8

Step-by-step explanation:

1. What is the difference?

The sequence goes down by 5. This means that the formula will have -5n in it.

2. Work out the term before the first term.

The first term is 3, and we know that the sequence goes up by 5. So, to get the term before 3 we would add 5.

3 + 5 = 8 Remember, this is positive 8. (+8)

3. Put that term at the end of the equation.

We have -5n already and we just worked out the term before the first one which is positive 8 - so put that at the end of the equation.

-5n + 8 This is our answer!

Just to prove it works:

Substitute: n = term

Lets see if we can get the 3rd term which is -7. (n = 3)

-5(3) + 8

-15 + 8 = -7

See, it works!

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Answer:

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3. $P(x) - Q(x)$ ---> $\frac{-2(12x - 5)}{(3x - 1)(-3x + 2)}$

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Step-by-step explanation:

Given that:

1. $P(x) = \frac{2}{3x - 1}$

$Q(x) = \frac{6}{-3x + 2}$

Thus,

$P(x)$ ÷ $Q(x)$ = $\frac{2}{3x - 1}$ ÷ $\frac{6}{-3x + 2}$

Flip the 2nd function, Q(x), upside down to change the process to multiplication.

$\frac{2}{3x - 1}*\frac{-3x + 2}{6}$

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Make both expressions as a single fraction by finding, the common denominator, divide the common denominator by each denominator, and then multiply by the numerator. You'd have the following below:

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$\frac{-6x + 4 + 18x - 6}{(3x - 1)(-3x + 2)}$

$\frac{-6x + 18x + 4 - 6}{(3x - 1)(-3x + 2)}$

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$\frac{-6x - 18x + 4 + 6}{(3x - 1)(-3x + 2)}$

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