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3 years ago

What is D of the arithmetic sequence for which a5 equals 24 and a9 equals 40

Mathematics

1 answer:

Gnom [1K]3 years ago

5 0

In an arithmetic sequence d represent the common difference.

The formula to find the general term of an arithmetic sequence is,

$a_{n} =a_{1} +(n-1)d$

Where $a_{n}$ = nth term and

$a_{1}$ = First term.

Given, $a_{5} = 24, a_{9} = 40$ . Therefore,

$a_{1} +(5-1)d = 24 , a_{1} +(9-1)d = 40$

$a_{1} +4d = 24 , a_{1} +8d = 40$

Next step is to subtract the above equations so that we can eliminate a1 and get the value of d. Hence,

4d - 8d = 24 - 40

-4d = - 16

$\frac{-4d}{-4}= \frac{-16}{-4}$ Divide each sides by - 16.

d = 4

So, d = 4.

Hope this helps yoi!.

You might be interested in

How many yards of the fencing materials do they need for the fence ? explain

labwork [276]

Answer:

152.7 yd

Step-by-step explanation:

I presume that there is a fence around the perimeter and separating the various plots.

AG = BF = CE = 18 yd

GH = DE = 12 yd

EO² = DE² + DO²

1 5² = 12² + DO²

225 = 144 + DO²

81 = DO²

DO = 9

BC = DO = EF = 9 yd

AC = DH = EG = 17 yd

AO² = AB² + BO² = 8² + 6² = 64 + 36 =100

AO = √100 = 10 yd

CO² = BC² + BO² = 9² + 6² = 81 + 36 = 127

CO = √127 yd

GO² = FG² + FO² = 8² + 12² =64 + 144 = 208

GO = √208 = 4√13 yd

Fencing needed

= (AC + DH + EG) + (AG + BF + CE) + AO + CO + EO + GO

= (3 × 17) + 3 × 18) + 10 + √127 + 15 + 4√13

= 51 + 54 + 25 + 11.27 + 14.42

= 152.7 yd

8 0

3 years ago

for every $2 kendra spent on materials, she could make 5 coasters. She made 60 coasters and sold them for the York Beach Fair, c

TEA [102]

Her profit was 126$ because she spent 24$ on her materials and then charged 5$ per 2 so you get 150$ then subtract the 24
(I think)

7 0

4 years ago

When you go to the store, does tax increase or decrease the cost of your items?

Musya8 [376]

yes because you have to pay more it's tricky

3 0

4 years ago

Question below

Ksivusya [100]

Answer:

$m \times H=\left[\begin{array}{c c c}\boxed{-9} & \boxed{36} & \boxed{-\dfrac{9}{2}}\end{array}\right]$

Step-by-step explanation:

Calculate the value of m

Given:

$3\left[\begin{array}{c c}-1 & 2 \\4 & 8\end{array}\right]=\dfrac{2}{3}m \times \left[\begin{array}{c c}-1 & 2 \\4 & 8\end{array}\right]$

Therefore:

$\implies 3=\dfrac{2}{3}m$

$\implies m=3 \times \dfrac{3}{2}$

$\implies m=\dfrac{9}{2}$

Calculate the value of H

Given:

$\left(H+ \left[\begin{array}{c c c}1 & 4 & -2\end{array}\right]\right)+\left[\begin{array}{c c c}3 & 2 & -6\end{array}\right]=\left[\begin{array}{c c c}-2 & 8 & -1\end{array}\right]+\left(\left[\begin{array}{c c c}1 & 4 & -2\end{array}\right]+\left[\begin{array}{c c c}3 & 2 & -6\end{array}\right]\right)$

Therefore:

$\implies H= \left[\begin{array}{c c c}-2 & 8 & -1\end{array}\right]$

Calculating m × H

$\implies m \times H=\dfrac{9}{2} \times \left[\begin{array}{c c c}-2 & 8 & -1\end{array}\right]$

$\implies m \times H=\left[\begin{array}{c c c}\dfrac{9}{2}(-2) & \dfrac{9}{2}(8) & \dfrac{9}{2}(-1)\end{array}\right]$

$\implies m \times H=\left[\begin{array}{c c c}-9 & 36 & -\dfrac{9}{2}\end{array}\right]$

7 0

2 years ago

John Davis makes $9.75 an hour. He works four hours on Monday, six hours on Tuesday, five hours on Wednesday, five hours on Thur

Hatshy [7]

You are given John Davis’ rate which is $9.75 an hour. It is said that he works for four hours on Monday, six hours on Tuesday, five hours on Wednesday, five hours on Thursday, and seven hours on Friday. You are asked to find the gross pay of John Davis. All you need to do is to multiply the rate to the hour of work.

Monday: $9.75(4h) = $39
Tuesday: $9.75(6h) = $58.5
Wednesday: $9.75(5h) = $48.75
Thursday: $9.75(5h) = $48.75
Friday: $9.75(7h) = $68.25

To get the gross pay, add everything and you will get $263.25. The answer is letter D.

8 0

3 years ago