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3 years ago

14

Write a real world situation the would represent -5 + -2 +3 = -4

1 answer:

Mariulka [41]3 years ago

7 0

Molly is in debt and owes the bank 5$, molly then buys a ice cream cone for 2$ with her credit card so now she is 7$ in debt aka she has -7 dollars in the bank. Molly then gives the bank 3$ in cash but she still owes the bank 4 dollars

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Determine formula of the nth term 2, 6, 12 20 30,42

nalin [4]

Check the forward differences of the sequence.

If $\{a_n\} = \{2,6,12,20,30,42,\ldots\}$ , then let $\{b_n\}$ be the sequence of first-order differences of $\{a_n\}$ . That is, for n ≥ 1,

$b_n = a_{n+1} - a_n$

so that $\{b_n\} = \{4, 6, 8, 10, 12, \ldots\}$ .

Let $\{c_n\}$ be the sequence of differences of $\{b_n\}$ ,

$c_n = b_{n+1} - b_n$

and we see that this is a constant sequence, $\{c_n\} = \{2, 2, 2, 2, \ldots\}$ . In other words, $\{b_n\}$ is an arithmetic sequence with common difference between terms of 2. That is,

$2 = b_{n+1} - b_n \implies b_{n+1} = b_n + 2$

and we can solve for $b_n$ in terms of $b_1=4$ :

$b_{n+1} = b_n + 2$

$b_{n+1} = (b_{n-1}+2) + 2 = b_{n-1} + 2\times2$

$b_{n+1} = (b_{n-2}+2) + 2\times2 = b_{n-2} + 3\times2$

and so on down to

$b_{n+1} = b_1 + 2n \implies b_{n+1} = 2n + 4 \implies b_n = 2(n-1)+4 = 2(n + 1)$

We solve for $a_n$ in the same way.

$2(n+1) = a_{n+1} - a_n \implies a_{n+1} = a_n + 2(n + 1)$

Then

$a_{n+1} = (a_{n-1} + 2n) + 2(n+1) \\ ~~~~~~~= a_{n-1} + 2 ((n+1) + n)$

$a_{n+1} = (a_{n-2} + 2(n-1)) + 2((n+1)+n) \\ ~~~~~~~ = a_{n-2} + 2 ((n+1) + n + (n-1))$

$a_{n+1} = (a_{n-3} + 2(n-2)) + 2((n+1)+n+(n-1)) \\ ~~~~~~~= a_{n-3} + 2 ((n+1) + n + (n-1) + (n-2))$

and so on down to

$a_{n+1} = a_1 + 2 \displaystyle \sum_{k=2}^{n+1} k = 2 + 2 \times \frac{n(n+3)}2$

$\implies a_{n+1} = n^2 + 3n + 2 \implies \boxed{a_n = n^2 + n}$

6 0

2 years ago

What is the answer?????/

SCORPION-xisa [38]

The questions is, when z=9, 3z = ? When you multiply 3*9, you get 27

3 0

4 years ago

Perlia paid for a dinner and left 20%, or $5.80, in tips. How much was the original bill (without counting the tip)?

klio [65]

Original bill is 100%/20% *5.8=29
(dollars)

3 0

3 years ago

Find the equation of a line that contains the points (4, -2) and (-8, -1). Write the equation in slope-intercept form, using

zmey [24]

Answer:

y =−12 /1 x−3 /5

8 0

3 years ago

Ind the perimeter of the figure. Round your answer to the nearest hundredth

ValentinkaMS [17]

Answer:

52.85

Step-by-step explanation:

perimeter of the rectangle is 40

perimeter of the half circle is 12.85

add those two together and get 52.85

MARK ME BRAINLIEST PLEASE

6 0

3 years ago