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3 years ago

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Critique Reasoning: A student says that the perimeter of a rectangle with side lengths (2x – 1) inches and 3x inches can be writ

ten as (5x - 1)
inches, because (2x – 1) + (3x) = 5x – 1. Explain why this statement is
incorrect.

1 answer:

elena-s [515]3 years ago

3 0

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Express the terms of the following sequence by giving a recursive formula.

emmasim [6.3K]

The recursive formula for given sequence is: $a_n = a_{n-1}-7$

And the terms will be expressed as:

$a_1 = 11\\a_2 = a_{2-1} - 7 \\a_2= a_1 - 7\\a_2 = 11- 7\\a_2 = 4\\a_3 = a_{3-1} - 7 \\a_3= a_2 - 7\\a_3 = 4 - 7\\a_3 = -3\\a_4 = a_{4-1} - 7 \\a_4= a_3 - 7\\ a_4= -3 - 7\\a_4 = -10\\a_5 = a_{5-1} - 7 \\a_5= a_4 - 7\\a_5 = -10 - 7\\a_5 = -17\\$

Step-by-step explanation:

First of all, we have to determine if the given sequence is arithmetic sequence or geometric. For that purpose, we calculate the common difference and common ratio

Given sequence is:

11,4,-3,-10,-17...

Here

$a_1 = 11\\a_2 = 4\\a_3 = -3\\So,\\d = a_2 - a_1 = 4-11 = -7\\d = a_3-a_2 = -3-4 = -7$

As the common difference is same, given sequence is an arithmetic sequence.

A recursive formula is a formula that is used to generate the next term of the sequence using the previous term and common difference

So, the recursive formula for an arithmetic sequence is given by:

$a_n = a_{n-1} +d\\Putting\ d = -7\\a_n = a_{n-1}-7$

Hence,

The recursive formula for given sequence is: $a_n = a_{n-1}-7$

And the terms will be expressed as:

$a_1 = 11\\a_2 = a_{2-1} - 7 \\a_2= a_1 - 7\\a_2 = 11- 7\\a_2 = 4\\a_3 = a_{3-1} - 7 \\a_3= a_2 - 7\\a_3 = 4 - 7\\a_3 = -3\\a_4 = a_{4-1} - 7 \\a_4= a_3 - 7\\ a_4= -3 - 7\\a_4 = -10\\a_5 = a_{5-1} - 7 \\a_5= a_4 - 7\\a_5 = -10 - 7\\a_5 = -17\\$

Keywords: arithmetic sequence, common difference

Learn more about arithmetic sequence at:

#LearnwithBrainly

6 0

4 years ago

Given the function g(x) = 6(4)x, Section A is from x = 0 to x = 1 and Section B is from x = 2 to x = 3.

Natasha2012 [34]

I also need this answer so when you find out let me know

5 0

3 years ago

Can anyone help me out, if you answer the question right i will give you a brainliest.

melisa1 [442]

Answer:

It's different because the experiment is more accurate as it progresses.

Step-by-step explanation:

You'll notice that the higher the numbers get in the experiment the closer it gets to your solution. The theoretical probability of flipping a coin is about 50% heads and 50% tails, but it doesn't always seem like that in an experiment. The experimental probability from your experimentation so far would be 62% of heads and 38% of tails.

4 0

3 years ago

Find the 14th term of the geometric sequence 2, 4, 8,

Papessa [141]

Answer:

16384

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

Liwen and Celina shared some plants in a ratio of 5:6. Celina decided to give Liwen 2/3 of her plants, which left her with 21 fe

djyliett [7]

Answer: 231

<u>Explanation:</u>

Liwen Celina

5x 6x

5x - 21 = $(\frac{2}{3})$ 6x

5x - 21 = 4x

<u>-4x +21</u> <u>-4x +21 </u>

x = 21

Liwen: 5x = 5(21) = 105

Celina: 6x = 6(21) =<u> 126</u>

Total: 231

6 0

3 years ago