There are 6 terms from term7 to term13
and the difference in their values is 109-43 = 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.
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!
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I think this way is a lot faster and easier to do by just quickly typing it all into the calculator, so thank you!
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