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3 years ago

12

Please please help me I have to finish and on question 2

1 answer:

Readme [11.4K]3 years ago

3 0

The answer is D

I’m pretty sure I hope it helped

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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

A 32-ounce tub of yogurt contains 5 servings. How many ounces of yogurt are in 1<br> serving?

Roman55 [17]

Answer:

32/5 ounces or approximately 6.4 ounces.

Step-by-step explanation:

We are trying to find the unit rate, so divide 32 by 5 to see how many ounces in just 1 serving.

7 0

3 years ago

Read 2 more answers

What is 14/5 as a mixed number ?

mash [69]

2 and 4/5 is 14/5 as a mixed number.

4 0

4 years ago

Read 2 more answers

PLS PLS PLS PLS HELPPPP

lesya [120]

<em>Answer: 62.4 computers or 62 </em>

<em />

<em>Step-by-step explanation:</em>

<em>Use this equation </em>

<em>48(n)</em>

<em>n will be 0.30 since the sales must increase by 30%</em>

<em>48(0.30)</em>

<em>14.4</em>

<em>Now add 48 and 14</em>

<em>48+14.4</em>

<em>62.4 or round it down to 62</em>

6 0

3 years ago

Estimate the amount of time the trip will take. 290 miles at 60 mph 5 hours 6 hours 4 hours 3 hours

Likurg_2 [28]

Answer:

It would take about 5 hours.

Step-by-step explanation:

Divide 290 miles and 60 mph to get 4.8 repeated.

Round 4.8 to get around 5 hours.

4 0

4 years ago