Answer:
3, -7, -17, -27, -37, -47
Step-by-step explanation:
Given: First term: a= 3 and Common Difference, d = -10
We need to find the first six term of the sequence.
Formula: ![a_n=a+(n-1)d](https://tex.z-dn.net/?f=a_n%3Da%2B%28n-1%29d)
where,
nth term of series
a is first term
n is number of term
d is common difference
For Second term, n=2
![a_2=3+(2-1)(-10) = 3-10=-7](https://tex.z-dn.net/?f=a_2%3D3%2B%282-1%29%28-10%29%20%3D%203-10%3D-7)
For Third term, n=3
![a_3=3+(3-1)(-10) = 3-20=-17](https://tex.z-dn.net/?f=a_3%3D3%2B%283-1%29%28-10%29%20%3D%203-20%3D-17)
For Fourth term, n=4
![a_4=3+(4-1)(-10) = 3-30=-27](https://tex.z-dn.net/?f=a_4%3D3%2B%284-1%29%28-10%29%20%3D%203-30%3D-27)
For Fifth term, n=5
![a_5=3+(5-1)(-10) = 3-40=-37](https://tex.z-dn.net/?f=a_5%3D3%2B%285-1%29%28-10%29%20%3D%203-40%3D-37)
For Sixth term, n=6
![a_6=3+(6-1)(-10) = 3-50=-47](https://tex.z-dn.net/?f=a_6%3D3%2B%286-1%29%28-10%29%20%3D%203-50%3D-47)
Hence, The sequence is 3, -7, -17, -27, -37, -47
The value of car after 12 years is $ 2982.92
<em><u>Solution:</u></em>
Given that,
A new car is purchased for 17000 dollars
The value of the car depreciates at 13.5% per year
<em><u>To find: Value of car after 12 years</u></em>
<em><u>The decreasing function is given as:</u></em>
![y = a(1-r)^t](https://tex.z-dn.net/?f=y%20%3D%20a%281-r%29%5Et)
Where,
y is the future value
a is the initial value
r is the decreasing rate in decimal
t is the number of years
From given,
![a = 17000\\\\t = 12\\\\r = 13.5 \% = \frac{13.5}{100} = 0.135](https://tex.z-dn.net/?f=a%20%3D%2017000%5C%5C%5C%5Ct%20%3D%2012%5C%5C%5C%5Cr%20%3D%2013.5%20%5C%25%20%3D%20%5Cfrac%7B13.5%7D%7B100%7D%20%3D%200.135)
<em><u>Substituting the values we get,</u></em>
![y = 17000(1-0.135)^{12}\\\\y = 17000(0.865)^{12}\\\\y = 17000 \times 0.1754661\\\\y = 2982.9241 \approx 2982.92](https://tex.z-dn.net/?f=y%20%3D%2017000%281-0.135%29%5E%7B12%7D%5C%5C%5C%5Cy%20%3D%2017000%280.865%29%5E%7B12%7D%5C%5C%5C%5Cy%20%3D%2017000%20%5Ctimes%200.1754661%5C%5C%5C%5Cy%20%3D%202982.9241%20%5Capprox%202982.92)
Thus value of car after 12 years is $ 2982.92
Answer:
235,236
Step-by-step explanation:
Answer:
The slope is <u>2</u>
Step-by-step explanation:
For this we use this slope formula
![\frac{y_{2}-y_{1} }{x_{2} -x_{1} }](https://tex.z-dn.net/?f=%5Cfrac%7By_%7B2%7D-y_%7B1%7D%20%7D%7Bx_%7B2%7D%20-x_%7B1%7D%20%7D)
These are our pairs
(8, 12) (16, 16)
x1 y1 x2 y2
![\frac{16-8}{16-12} = \frac{8}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B16-8%7D%7B16-12%7D%20%3D%20%5Cfrac%7B8%7D%7B4%7D)
8/4=2
<u> M=2</u>
<span>It is effective support for the claim. Hope this helps</span>