4.
![a_1=-20,\ a_3=-15\\\\2d=a_3-a_1\to 2d=-15-(-20)\to2d=-15+20\to2d=5\to d=2.5\\\\a_n=a_1+(n-1)d\to a_n=-20+(n-1)(2.5)=-20+2.5n-2.5=2.5n-22.5\\\\a_2=2.5(2)-22.5=5-22.5=-17.5\\\\a_4=2.5(4)-22.5=10-22.5=-12.5\\\\a_6=2.5(6)-22.5=15-22.5=-7.5](https://tex.z-dn.net/?f=a_1%3D-20%2C%5C%20a_3%3D-15%5C%5C%5C%5C2d%3Da_3-a_1%5Cto%202d%3D-15-%28-20%29%5Cto2d%3D-15%2B20%5Cto2d%3D5%5Cto%20d%3D2.5%5C%5C%5C%5Ca_n%3Da_1%2B%28n-1%29d%5Cto%20a_n%3D-20%2B%28n-1%29%282.5%29%3D-20%2B2.5n-2.5%3D2.5n-22.5%5C%5C%5C%5Ca_2%3D2.5%282%29-22.5%3D5-22.5%3D-17.5%5C%5C%5C%5Ca_4%3D2.5%284%29-22.5%3D10-22.5%3D-12.5%5C%5C%5C%5Ca_6%3D2.5%286%29-22.5%3D15-22.5%3D-7.5)
<u>n | 1 | 2 | 3 | 4 | 5 | 6 |</u>
f(n)| -20 | -17.5 | -15 |-12.5| -10 | -7.5 |
First term: -20 Common Difference: 2.5
Explicit Rule:
Recursive Rule: ![a_1=-20,\ a_n=a_{n-1}+2.5](https://tex.z-dn.net/?f=a_1%3D-20%2C%5C%20a_n%3Da_%7Bn-1%7D%2B2.5)
5.
![a_1=123,\ a_2=131\\\\d=a_2-a_1\to d=131-123=8\\\\a_n=a_1+(n-1)d\to a_n=123+(n-1)(8)=123+8n-8=8n+115\\\\a_3=8(3)+115=24+115=139\\\\a_5=8(5)+115=40+115=155\\\\a_6=8(6)+115=48+115=163](https://tex.z-dn.net/?f=a_1%3D123%2C%5C%20a_2%3D131%5C%5C%5C%5Cd%3Da_2-a_1%5Cto%20d%3D131-123%3D8%5C%5C%5C%5Ca_n%3Da_1%2B%28n-1%29d%5Cto%20a_n%3D123%2B%28n-1%29%288%29%3D123%2B8n-8%3D8n%2B115%5C%5C%5C%5Ca_3%3D8%283%29%2B115%3D24%2B115%3D139%5C%5C%5C%5Ca_5%3D8%285%29%2B115%3D40%2B115%3D155%5C%5C%5C%5Ca_6%3D8%286%29%2B115%3D48%2B115%3D163)
<u>n | 1 | 2 | 3 | 4 | 5 | 6 |</u>
f(n)| 123 | 131 | 139 | 147 | 155 | 163 |
First term: 123 Common Difference: 8
Explicit Rule:
Recursive Rule: ![a_1=20,\ a_n=a_{n-1}+8](https://tex.z-dn.net/?f=a_1%3D20%2C%5C%20a_n%3Da_%7Bn-1%7D%2B8)
9514 1404 393
Answer:
- boat: 72 km/h
- current: 16 km/h
Step-by-step explanation:
The speed difference between boat and current is the upstream rate:
(448 km)/(8 h) = 56 km/h
The sum of speeds of boat and current is the downstream rate:
(440 km)/(5 h) = 88 km/h
The rate of the boat is half the sum of these:
(56 +88)/2 = 72 . . . km/h
The rate of the current is half their difference:
(88 -56)/2 = 16 . . . km/h
The rate of the boat is 72 km/h; the rate of the current is 16 km/h.
25.20, that might help you hopefully!
Answer:
Step-by-step explanation:i wanted to ask this questionWhich property of metals is Luis most likely going to demonstrate using these materials