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1. Which formula defines the sequence f(1)=2, f(2)= 6, f(3)= 10, f(4)= 14, f(5)= 18?

Natasha_Volkova [10]

Answer:

$f(n) =4 + f(n-1) \\for\ n>2$

Step-by-step explanation:

Given

$f(1)=2\\ f(2)= 6\\ f(3)= 10\\ f(4)= 14\\ f(5)= 18$

Required

Determine the formula

First, we need to solve common difference (d)

$d = f(n) - f(n-1)$

Take n as 2

$d = f(2) - f(2-1)$

$d = 6 - 2$

$d = 4$

Represent each function as a sum of the previous

$f(1) = 2$

$f(2) = 2 + 4 = f(1) + 4$

$f(3) = 6 + 4 = f(2) + 4$

$f(4) = 10 + 4 = f(3) + 4$

$f(5) = 14 + 4 = f(4) + 4$

Represent the function as $f(n)$

$f(n) =f(n-1) + 4$

Reorder

$f(n) =4 + f(n-1) \\for\ n>2$

7 0

2 years ago

Paula, a college student, earned $3,600 one summer. During the following semester, she spent $2,500 for tuition, $650 for rent,

Softa [21]

So to get the $ spent on misc items, just add up the other expenses and subtract it from 3600:

$2500+650+430=3580\\ \\ 3600-3580=\$ 20$

Now to put them into fractions.

Tuition: $\frac{2500}{3600}=\frac{25}{36}$

Rent: $\frac{650}{3600}=\frac{65}{360}$

Food: $\frac{430}{3600}=\frac{43}{360}$

Misc: $\frac{20}{3600}=\frac{1}{180}$

8 0

1 year ago

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2.Use common sense to determine whether the given event is possible. You are the one-millionth customer at a local hardware stor

Misha Larkins [42]

2. it is possible, but unlikely
3. a university

6 0

2 years ago

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Write the rational number as a decimal. −18/5

Angelina_Jolie [31]

Answer:

-3.6

Step-by-step explanation:

When plugged into a calculator, the answer turns out to be -3.6, which is a decimal.

6 0

1 year ago

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Zach read a book for 10 minutes every weekend in the first month, 20 minutes in the second month, 40 minutes in the third month,

den301095 [7]

Zach time of reading every weekend forms a sequence with these terms: 10, 20, 40, 80. On the other hand, that of Victoria forms a sequence with terms: 35, 50, 65, 80. By keenly observing the sequences, Zach's sequence is a geometric sequence with a common ratio equal to 2 and Victoria's sequence is an arithmetic or linear sequence with a common difference of 15. Thus, the answer is letter B.

5 0

1 year ago

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