To find the 7th term, all you have to do is plug it in the equation.
First n would equal 7 because we are looking for the 7th term.
Now, let's plug everything we know into the equation.
a7 = 2+5 * (7-1)
= 2 + 5 * 6
= 2 + 30
= 32
In conclusion, the 7th term would equal 32.
This revolves around exact trig values - no easy way to say this, you just need to memorise them. They are there for sin cos and tan, but I will give you the main tan ones below - note this is RADIANS (always work in them when you can, everything is better):
tan0: 0
tanpi/6: 1/sqrt(3)
tanpi/4: 1
tanpi/3: sqrt(3)
tanpi/2: undefined
Now we just need to equate -2pi/3 to something we understand. 2pi/3 is 1/3 of the way round a circle, so -2pi/3 is 1/3 of the way round the circle going backwards (anticlockwise), so on a diagram we already know it's in the third quadrant of the circle (somewhere between pi and 3pi/2 rads).
We also know it is pi/3 away from pi, so we are looking at sqrt(3) or -sqrt(3) because of those exact values.
Now we just need to work out if it's positive or negative. You can look up a graph of tan and it'll show that the graph intercepts y at (0,0) and has a period of pi rads. Therefore between pi and 3pi/2 rads, the values of tan are positive. Therefore, this gives us our answer of sqrt(3).
Answer:
The intersection of both lines.
2y - 18x = -26
Add 18x to both sides.
2y = -26 + 18x
Divide by 2 on both sides.
y = -13 + 9x
y = 9x - 13
