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Elina [12.6K]
3 years ago
14

The first four terms of a sequence are \text{3, -6, 12, -24}. Write an explicit formula for this sequence, where n is any term n

umber and a\left(n\right) is the nth term.
Mathematics
1 answer:
user100 [1]3 years ago
4 0

You can see that each term is twice the previous one, with inverted sign.

You double a number by multiplying it by two, and you change its sign by multiplying it by -1.

So, you multiply each term by 2 and by -1, which results in a multiplication by -2.

Since we start with 3, the terms are

a_1 = 3

a_2 = 3\cdot (-2) = -6

a_3 = -6\cdot (-2) = 12

and so on. So, the general term is

a_n = 3\cdot(-2)^{n-1}

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Answer:

g(x) = x+5

Step-by-step explanation:

Given that,

f(x)=x^4+5x^3-3x-15

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We need to find the polynomial. We know that, Euclid division lemma states that

f(x)=q(x)\times g(x)+r(x)

Where

f(x) is dividend

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r(x) is remainder

So,

x^4+5x^3-3x-15=(x^3-3)\times g(x) +0\\\\g(x)=\dfrac{x^4+5x^3-3x-15}{(x^3-3)}\\\\g(x)=x+5

So, the polynomial is (x+5).

 

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