CPhill

1/4 + 1/2   =

1/4  +  2/4  =

3/4

LOL!!!

Yep.....It would have helped to supply the link  :

https://www.desmos.com/calculator/2thymd2pwe

We can solve this system....where a1 is the first term and d is the common difference between terms

30   =  a1 + 6d         

60  =  a1  + 10d

Subtract the 1st equation from the 2nd

30  =  4d       divide both sides by 4

7.5  =  d

And using the second equation to find a1, we have

60  =  a1  + 10(7.5)

60  = a1  +  75           subtract 75 from both sides

-15    =  a1

So......the 21st term is

-15 + 7.5(20)  =

135

Don't see any solution presented, but.....it will lie in the over-lapping shaded regions shown here :

Thanks, X².....!!!!

1.  I used this tool to generate the best-fit line :

http://www.alcula.com/calculators/statistics/linear-regression/

 The generated equation  is   about   y =  1x  + 3.26   which is closest to

 y  = x + 3    ........So....hectictar's answer is good

2.  This looks to be almost linear.....the best fit appars to be  y  = 2x -1......as hectictar said

3. This is the same graph as 2.....  so.....2(12) - 1  = 23.......

"22"  seems to be the closest value

4. Very difficult to tell what the exact values are, but hectictar's logic seems sound.....!!!!

2  = 3/4  + x        subtraction property of equality

2 - 3/4  =  3/4 - 3/4  + x

2 - 3/4   =  x

8/4 -  3/4  =  x

5/4  =  x

0.3x  = 4.5

(3/10)x  =  4 + 1/2

(3/10)x  =  9/2          multiply through by  10/3

x   =  (9/2) (10/3)   =   90 / 6     =   15

Wow, ZZZ......those ARE  cool!!!!!

Thanks for sharing !!!!

I'm afraid I'll have to join Melody, here.....I don't know how to solve this "by hand"

For what it's worth......here's the graphical solution :

https://www.desmos.com/calculator/9w8cvwjb3y