Posted by Crystal on .
Determine the sum of the first 20 terms of the arithmetic sequence in which ...
f) the 7th term is 43 and the 13th term is 109
I know you can make two equations :
43 = a + 6d and 109 = a + 12 d
And subtract them to get d = 11
But I know there's another way to get d, that you can just quickly do on your calculator. But I can't remember how to do it! It had something to do with dividing the number of terms or something...? I could probably figure it out after some trial and error but I just want to make sure I have the proper method down, so if someone could explain a clear and concise method to me, I would really appreciate it! I know it's really simple... I'm just so burned out right now. Too much studying, too much stress!

Math 
Reiny,
There are 6 terms from term7 to term13
and the difference in their values is 10943 = 66
so the common difference is 66/6 = 11
but, ... , notice that you are actually doing the same calculations you would do if you solved the two equations, so nothing gained. 
Math 
Crystal,
I think this way is a lot faster and easier to do by just quickly typing it all into the calculator, so thank you!