85, 87, and 89 are the integers
I hope this helps you
-2/2t+4w=6
-4t-8w= -12
4t+6w=15
-2w=3
w= -3/2
2t-4.3/2=6
2t=12
t=6
Answer:
The equation for the nth term of the given arithmetic sequence is: ![\mathbf{a_n=13n+22}](https://tex.z-dn.net/?f=%5Cmathbf%7Ba_n%3D13n%2B22%7D)
Step-by-step explanation:
We need to write an equation for the nth term of the arithmetic sequence:
15,28,41 ....
The equation for arithmetic sequence is: ![a_n=a_1+(n-1)d](https://tex.z-dn.net/?f=a_n%3Da_1%2B%28n-1%29d)
Where
is the nth term,
is first term and d is common difference
In the given sequence we have:
a₁ = 15
a₂ = 28
We can find common difference using the formula:
![a_n=a_1+(n-1)d\\Put\: n=2, a_2=28\: and\: a_1=15\\a_2=a_1+(2-1)d\\28=15+d\\d=28-15\\d=13](https://tex.z-dn.net/?f=a_n%3Da_1%2B%28n-1%29d%5C%5CPut%5C%3A%20n%3D2%2C%20a_2%3D28%5C%3A%20and%5C%3A%20a_1%3D15%5C%5Ca_2%3Da_1%2B%282-1%29d%5C%5C28%3D15%2Bd%5C%5Cd%3D28-15%5C%5Cd%3D13)
So, the common difference d is 13
Now, equation for nth term will be:
![a_n=a_1+(n-1)d\\Put\:a_1=15, d=13\\a_n=15+(n-1)13\\Solving:\\a_n=15+13n-13\\a_n=13n+2](https://tex.z-dn.net/?f=a_n%3Da_1%2B%28n-1%29d%5C%5CPut%5C%3Aa_1%3D15%2C%20d%3D13%5C%5Ca_n%3D15%2B%28n-1%2913%5C%5CSolving%3A%5C%5Ca_n%3D15%2B13n-13%5C%5Ca_n%3D13n%2B2)
So, the equation for the nth term of the given arithmetic sequence is: ![\mathbf{a_n=13n+22}](https://tex.z-dn.net/?f=%5Cmathbf%7Ba_n%3D13n%2B22%7D)
where n=1,2,3..
Answer:
3x+2/4>-20
3x+2>-80
3x>-80-2
3x>-82
x>-82/3
Also simplified to, x>-27 1/3