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2 years ago

Yeah I didn't pay attention today

Mathematics

1 answer:

Marina CMI [18]2 years ago

8 0

Answer: 314.3

Explanation: multiply 449 by .30 and then subtract your solution of that to 449 and you will have your new sum

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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

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

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2 years ago

What is the value of x in the recntangle (2 1/2+ X) cm and 2 1/2 cm

vaieri [72.5K]

Answer:

Step-by-step explanation:

Given that:

Length (l) = 13 cm

Width (w) = 8 cm

Perimeter of the rectangle = 2(l + w) units

P = 2(13 + 8)

P = 2 (21)

P = 42

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2 years ago

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tatyana61 [14]

Answer:

Step-by-step explanation:

3 hours per basket

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Answer:

3^7 x 1/3^4; in other words the first choice

Step-by-step explanation:

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3 years ago

7+a=10;3,13,17 branlest

Assoli18 [71]

Answer:

Step-by-step explanation:

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Yeah I didn't pay attention today ​

Yeah I didn't pay attention today