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Gennadij [26K]
3 years ago
11

Find the third fourth and fifth terms of the sequence defined by a1=1, a2=3, and a n =(-1)n a n-2 for n>3

Mathematics
1 answer:
Maslowich3 years ago
5 0

We have been given that

a_1=1\\  a_2=3\\
a_ n =(-1)^n a _{n-2} \text{ for } n>3

In order to find the third term, we substitute n=3

a_ 3 =(-1)^3a _{(3-2)}\\
\\
a_ 3 =(-1)^3 a _{1}

Substituting the given value of a_1

a_ 3 =(-1)^3 \times 1\\
\\
a_3=-1\times 1\\
\\
a_3=-1

Similarly, we can find the fourth term by plugging n=4

a_ 4 =(-1)^4a _{(4-2)}\\
\\
a_ 4 =(-1)^4 a _{2}\\
\\
a_4= 1\times 3\\
\\
a_4=3

Therefore, the third term is -1

And the fourth term is 3


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x_1+x_2=6\\\\
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=\frac{6\pm\sqrt{-24}}{2}=\frac{6\pm2\sqrt{-6} }{2}=3\pm i\sqrt{6}\\\\
x_1=\boxed{3-i\sqrt{6}}\\\\
x_2=\boxed{3+i\sqrt{6}}\\\\
\texttt{Verify:}\\\\
x_1+x_2=3-\underline{i\sqrt{6}}+3+\underline{i\sqrt{6}}=3+3=6~~correct\\\\
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4 0
4 years ago
The volume of a cylinder is 1323pi cmcubed. The radius of the base of the cylinder is 7 cm. What is the height of the​ cylinder?
Taya2010 [7]
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4 0
3 years ago
Find the missing probability.<br> P(A) = 0.4; P(B) = 0.7; P(A or B)<br> ; P(A and B) = 0.3
solong [7]

Given:

P(A)=0.4, P(B)=0.7, P(A\text{ and }B)=0.3

To find:

The value of P(A\text{ or }B).

Solution:

We know that,

P(A\text{ and }B)=P(A\cap B)

P(A\text{ or }B)=P(A\cup B)

It means, we have P(A)=0.4, P(B)=0.7, P(A\cap B)=0.3 and we need to find the value of  P(A\cup B).

P(A\cup B)=P(A)+P(B)-P(A\cap B)

P(A\cup B)=0.4+0.7-0.3

P(A\cup B)=1.1-0.3

P(A\cup B)=0.8

Therefore, the value of P(A\text{ or }B) is 0.8.

4 0
3 years ago
In expression 8x, what is 8 to x
Ksivusya [100]
I'm not sure if this is the answer you are looking for, but the number before a variable is called a coefficient.  
4 0
3 years ago
Please someone help me with this
gregori [183]

Answer:

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Step-by-step explanation:

<u>Full surface area:</u>

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3 0
3 years ago
Read 2 more answers
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