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vaieri [72.5K]
3 years ago
6

What are the first four terms of the sequence defined recursively below

Mathematics
2 answers:
Effectus [21]3 years ago
4 0
At n = 2
a₂ = (-1)² + 3a₂₋₁ + 2
a₂ = 1 + 3a₁ + 2
a₂ = 1 + (3)(5) + 2
a₂ = 18

At n = 3
a₃ = (-1)³ + 3a₃₋₁ + 2
a₃ = -1 + 3a₂ + 2
a₃ = -1 + (3)(18) + 2
a₃ = 55

At n = 4
a₄ = (-1)⁴ + 3a₄₋₁ + 2
a₄ = 1 + 3a₃ + 2
a₄ = 1 + (3)(55) + 2
a₄ = 168

The first four terms are 5, 18, 55, 168




NikAS [45]3 years ago
4 0

Answer:

The first four terms are 5, 18, 55, 168

Step-by-step explanation:

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Rama09 [41]

Answer:

?

Step-by-step explanation:

Problem 1

Sketch or describe the figure in Step 4 and Step 15.

Pattern of small squares. Step 1 has 1 square. Step 2 has 4 squares, 2 by 2 with bottom left square moved to top right corner. Step 3 has 9 squares, 3 by 3 with bottom left moved to top right corner.

How many small squares will there be in each of these steps?

Write an equation to represent the relationship between the step number, , and the number of small squares, , in each step.

Explain how your equation relates to the pattern.

Problem 2

Which expression represents the relationship between the step number  and the total number of small squares in the pattern?

A pattern of small squares. Step 1 has 0 squares. Step 3 has 3 squares: 2 by 2 but missing the lower right square. Step 3 has 8 squares: 3 by 3 but missing the lower right square.

A:

B:

C:

D:

Problem 3

Each figure is composed of large squares and small squares. The side length of the large square is . Write an expression for the area of the shaded part of each figure.

Figure A

Large square with 1 by 1 small squares removed from each corner.

Figure B

2 large squares side by side. On the side of the right square, there are 2 small squares stacked vertically, each with dimensions 2 by 2.

Problem 4

Here are a few pairs of positive numbers whose difference is 5.

Find the product of each pair of numbers. Then, plot some points to show the relationship between the first number and the product.

first

number second

number product

1 6  

2 7  

3 8  

5 10  

7 12  

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Is the relationship between the first number and the product exponential? Explain how you know.

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Here are some lengths and widths of a rectangle whose perimeter is 20 meters.

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1 9  

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5    

7    

9    

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On the coordinate plane, plot the points for length and area from your table.

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A blank graph, origin O, with a grid.

Problem 6

Here is a pattern of dots.

Four figures, labeled step 0 through 3. Step 0, row with 1 dot. Step 1, row with 2 dots. Step 2, row with 2 dots above row with 3 dots. Step 3, 2 rows of 3 dots above row with 4 dots.

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Mai has a jar of quarters and dimes. She takes at least 10 coins out of the jar and has less than $2.00.

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6 0
3 years ago
T+2=7<br> t= <br> Please help with this
anygoal [31]

Answer:

t = 5

Step-by-step explanation:

Given

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7 0
3 years ago
Read 2 more answers
The product of the ages of a man and his son is 160. In four years time, the man will be four times as old as his son. Find thei
kati45 [8]

Answer:

father = 32    s = 5 y/o

Step-by-step explanation:

f s = 160  ====>   s = 160/f

f+4 = 4 ( s+4)  

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f^2 + 4f = 640 + 16 f

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3 0
1 year ago
Read 2 more answers
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