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2 years ago

14

In an arithmetic sequence, a17 = -40 anda28 = -73. Explain how to use this information to write a recursive formula for this seq

uence.

1 answer:

ohaa [14]2 years ago

4 0

Answer:

–73 – (–40) = –33.

Step-by-step explanation:

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Jennifer wants to purchase a book but only has $62.10 to spend. What is the maximum number of pages she can have in her book if

nevsk [136]

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3 years ago

A shoe company got an order for 3 cartons of shoes. There are 42 pairs of

erik [133]

Answer:

126?

Step-by-step explanation:

sense there are 3 cartons and 42 in each carton you would multiply 3 by 42 to get 126.

6 0

2 years ago

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 6 divide by 5

lara31 [8.8K]

Hey there!

6 divided by 5 = 1.2

Hope this helps!
Have a great day! (:

7 0

3 years ago

What is 3/10 ÷5/10 ?

olasank [31]

The answer is 30/50 look below:
KCF keep change flip
so keep the first one the way it is
change the sign to multiplication from division
filp the 2nd fraction into a improper fraction
than multiply
so...
3*10=30
10*5=50
so...
your answer is 30/50 or 3/5 that is in simplest form

Hope this helped

5 0

3 years ago