3 years ago

What does interperate slope in context mean?

Mathematics

1 answer:

Salsk061 [2.6K]3 years ago

3 0

Answer:

Interpret the slope of a line as the change in y when x changes by 1.

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Find the general term of {a_n}

Assoli18 [71]

From the given recurrence, it follows that

$a_{n+1} = 2a_n + 1 \\\\ a_{n+1} = 2(2a_{n-1} + 1) = 2^2a_{n-1} + 1 + 2 \\\\ a_{n+1} = 2^2(2a_{n-2}+1) + 1 + 2 = 2^3a_{n-2} + 1 + 2 + 2^2 \\\\ a_{n+1} = 2^3(2a_{n-3} + 1) + 1 + 2 + 2^2 = 2^4a_{n-3} + 1 + 2 + 2^2 + 2^3$

and so on down to the first term,

$a_{n+1} = 2^na_1 + \displaystyle \sum_{k=0}^{n-1}2^k$

(Notice how the exponent on the 2 and the subscript of a in the first term add up to n + 1.)

Denote the remaining sum by S ; then

$S = 1 + 2 + 2^2 + \cdots + 2^{n-1}$

Multiply both sides by 2 :

$2S = 2 + 2^2 + 2^3 + \cdots + 2^n$

Subtract 2S from S to get

$S - 2S = 1 - 2^n \implies S = 2^n - 1$

So, we end up with

$a_{n+1} = 4\cdot2^n + S \\\\ a_{n+1} = 2^2\cdot2^n + 2^n-1 \\\\ a_{n+1} = 2^{n+2} + 2^n - 1 \\\\\implies \boxed{a_n = 2^{n+1} + 2^{n-1} - 1}$

5 0

2 years ago

30 boxes of melons and 4 melons in each bag . Each bag holds two melons. How melons are there in the store.

SVEN [57.7K]

The answer is the store has 240 melons.
(30x4)x2=240

8 0

3 years ago

Will give brainliest for correct answer.

lukranit [14]

The numerator and denominator must be polynomials so

the answer to your question is - 7x / x^2 ( the last one on the right)

5 0

3 years ago

Read 2 more answers

help At 1:00 P.M. the water level of a pool is 13 inches At 1:30 P.M. the water level is 18 inches At 2:30 the water level is 28

mamaluj [8]

The answer is 5 . because if you count the # it will go to 28

7 0

3 years ago

Suppose you make hot chocolate. It's too hot to drink, so you put it in the freezer to cool it off. If the original temperature

grandymaker [24]

Answer:

B.) 132.56 degrees

Step-by-step explanation:

8 0

2 years ago