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raketka [301]
3 years ago
14

5. (5 points) Write the first 5 terms of the sequence if a1 = 9 and an-1 +n

Mathematics
1 answer:
Ivanshal [37]3 years ago
6 0

Answer:

9,4,-1,-6,-11

Step-by-step explanation:

When n = 1: a(1+1) =a(1) +1

                   a(2) = -9 +1

                   a(2) = -8

When n = 2: a(2+1) =a(2) + 2

                   a(3) = -8 + 2

                    a(3) = -6

When n = 3: a(3+1) = -6 + 3

a(4) = -3

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Among the four choices, (x + 5) is the only one that is not a linear factor of this polynomial function.

Step-by-step explanation:

Let a denote some constant. A linear factor of the form (x - a) is a factor of a polynomial f(x) if and only if f(a) = 0 (that is: replacing all x in the polynomial f(x) \! with the constant a\! would give this polynomial a value of 0.)

For example, in the second linear factor (x - 2), the value of the constant is a = 2. Verify that the value of f(2) is indeed 0. (In other words, replacing all x in the polynomial f(x) \! with the constant 2 should give this polynomial a value of 0\!.)

\begin{aligned}f(2) &= 2^3 - 5\times 2^2 - 4 \times 2 + 20 \\ &= 8 - 20 - 8 + 20 \\ &= 0 \end{aligned}.

Hence, (x - 2) is indeed a linear factor of polynomial f(x).

Similarly, it could be verified that (x - 5) and (x + 2) are also linear factors of this polynomial function.

Rewrite the first linear factor (x + 5) in the form (x - a) for some constant a: (x + 5) = (x - (-5)), where a = -5.

Calculate the value of f(5).

\begin{aligned}f(5) &= (-5)^3 - 5\times (-5)^2 - 4 \times (-5) + 20 \\ &= (-125) - 125 + 20 + 20 \\ &= -210\end{aligned}.

f(5) \ne 0 implies that (x - (-5)) (which is equivalent to (x + 5)) isn't a linear factor of this polynomial function.

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The simplified form of the equation is 4.4x + 1.5.

Given

Equation; (1.6x + 7.3) + (–0.6x + 2) – (7.8 – 3.4x)

<h3>Addition</h3>

The addition is the process of adding things together.

To simplify the equation follow all the steps given below.

First, open the brackets combine like terms, and simplify.

Then,

The equation in simplified form is;

\rm  (1.6x + 7.3) + (-0.6x + 2) - (7.8 -3.4x)\\\\1.6x+7.3-0.6x+2-7.8+3.4x\\\\1.6x-0.6+3.4x+7.3-7.8\\\\4.4x+1.5

Hence, the simplified form of the equation is 4.4x + 1.5.

To know more about addition click the link given below.

brainly.com/question/15892196

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