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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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Answer: Polygon Q's area is 1/4 of Polygon P's area

======================================================

Explanation:

Imagine we had a square with side length 8. The area of this square is 8*8 = 64.

Now let's reduce each side of the square by the scale factor 1/2. So each new side is 8*(1/2) = 4. The area of this smaller square is 4*4 = 16.

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So this is one example to see why (1/2)*(1/2) = 1/4 is the area scale factor based on the linear scale factor of 1/2. In short, (1/2)^2 = 1/4. Whatever the original scale factor is, square it and you'll get the area scale factor.

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Answer:

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Step-by-step explanation:

For this case we can use the formula for the future value with compound interest given by:

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So then the balance after 6 years would be approximately 50995 with the conditions provided.

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