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3 years ago

Find the first five terms of the sequence. an=-n2+2n

Mathematics

2 answers:

dedylja [7]3 years ago

8 0

Answer:

The first five terms of the given sequence is 1, 0, -3, -8, -15

Step-by-step explanation:

Given: nth term of sequence $a_n=-n^2+2n$

We have to find the first five terms of the given sequence,

Consider the given nth term of sequence $a_n=n^2+2n$

Substitute n = 1 ,

we get, $a_1=-(1)^2+2=-1+2=1$

Substitute n = 2 ,

we get, $a_2=-(2)^2+2(2)=-4+4=0$

Substitute n = 3,

we get, $a_3=-(3)^2+2(3)=-9+6=-3$

Substitute n = 4 ,

we get $a_4=-(4)^2+2(4)=-16+8=-8$

Substitute n = 5 ,

we get $a_5=-(5)^2+2(5)=-25+10=-15$

Thus, first five terms of the given sequence is 1, 0, -3, -8, -15

Julli [10]3 years ago

3 0

If your sequence is this

$an = - {n}^{2} + 2n \\ then \\ a1 = - 1 + 2 = 1 \\ a2 = - 4 + 4 = 0 \\ a3 = - 9 + 6 = - 3 \\ a4 = - 16 + 8 = - 8 \\ a5 = - 25 + 10 = - 15$

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X + 2y – 4z = 1 -2x – 4y + 4z = 6 -4x – 3y – 4z = 21

elena55 [62]

Answer:

x = - 1

y = - 3

z = -2

Step-by-step explanation:

Please see steps in the image attached here.

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3 years ago

Need answer fast with all the steps included please

wel

Answer:

6n²√3

Step-by-step explanation:

2√3n•√9n³

The above expression can be simplified as follow:

Recall

√9 = 3

2√3n•√9n³ = 2√3n × 3√n³

Recall

m√a × n√b = mn√(a × b)

Thus,

2√3n × 3√n³ = (2×3) √(3n × n³)

2√3n × 3√n³ = 6√3n⁴

Recall:

√aᵇ = (aᵇ)¹/² = aᵇ/²

√n⁴ = n⁴/²

√n⁴ = n²

Thus,

6√3n⁴ = 6n²√3

Therefore,

2√3n•√9n³ = 6n²√3

4 0

3 years ago

D.sqrt(2+x^/2) Solve this question please

lidiya [134]

Answer:

Option a.

Step-by-step explanation:

By looking at the options, we can assume that the function y(x) is something like:

$y = \sqrt{4 + a*x^2}$

$y' = (1/2)*\frac{1}{\sqrt{4 + a*x^2} }*(2*a*x) = \frac{a*x}{\sqrt{4 + a*x^2} }$

such that, y(0) = √4 = 2, as expected.

Now, we want to have:

$y' = \frac{x*y}{2 + x^2}$

replacing y' and y we get:

$\frac{a*x}{\sqrt{4 + a*x^2} } = \frac{x*\sqrt{4 + a*x^2} }{2 + x^2}$

Now we can try to solve this for "a".

$\frac{a*x}{\sqrt{4 + a*x^2} } = \frac{x*\sqrt{4 + a*x^2} }{2 + x^2}$

If we multiply both sides by y(x), we get:

$\frac{a*x}{\sqrt{4 + a*x^2} }*\sqrt{4 + a*x^2} = \frac{x*\sqrt{4 + a*x^2} }{2 + x^2}*\sqrt{4 + a*x^2}$

$a*x = \frac{x*(4 + a*x^2)}{2 + x^2}$

We can remove the x factor in both numerators if we divide both sides by x, so we get:

$a = \frac{4 + a*x^2}{2 + x^2}$

Now we just need to isolate "a"

$a*(2 + x^2) = 4 + a*x^2$

$2*a + a*x^2 = 4 + a*x^2$

Now we can subtract a*x^2 in both sides to get:

$2*a = 4\\a = 4/2 = 2$

Then the solution is:

$y = \sqrt{4 + 2*x^2}$

The correct option is option a.

7 0

2 years ago

I have a question what is 12•3

Free_Kalibri [48]

12•3=36 it help you have a great fay

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2 years ago

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vazorg [7]

A. 1 7/5 is the answer

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3 years ago

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