Math
posted by Crystal .
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!

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. 
I think this way is a lot faster and easier to do by just quickly typing it all into the calculator, so thank you!
Respond to this Question
Similar Questions

Precalculus
The 8th term in an arithmetic sequence is 5, and the sum of the first 10 terms is 20. Find the common difference and the first term of the sequence. Alright so in an arithmetic squence the difference d between any two successive numbers … 
Math *URGENT
Please give the answers and solutions for each. 1.If the second term is 2 and the seventh term of a geometric sequence is 64, find the 12th term. 2. Which term if the geometric sequence 18,54,162,486,... is 3,188,646? 
Can someone help me?!
The 1st, 5th and 13th terms of an arithmetic sequence are the first three terms of a geometric sequence with a common ratio 2. If the 21st term of the arithmetic sequence is 72, calculate the sum of the first 10 terms of the geometric … 
Maths
1..The first 2 terms of a geometric progression are the same as the first two terms of an arithmetic progression.The first term is 12 and is greater than the second term.The sum of the first 3 terms od the arithmetic progression is … 
Algebra
True or False 1. – 5, – 5, – 5, – 5, – 5, … is an arithmetic sequence. 2. In an arithmetic sequence, it is possible that the 13th term is equal to its 53rd term. 3. In an arithmetic sequence, the common difference is computed … 
Mathematics arithmetic sequence
The sum of second and sixth terms of an arithmetic sequence is 4. The third term is 24 more than eleventh term. So determine the first three terms of the sequence. 
math
in an arithmetic sequence the common difference is equal to 2.the first term is also the first term of a geometric sequence. the sum of the first 3 terms of an arithmetic sequence and the sum of the first 9 terms of an arithmetic sequence … 
math
The 1st,5th,13th term of an arithmetic sequence are the first 3 terms of geometric sequence with a common ratio of 2. If the 21st term of the arithmetic sequence is 72, calculate the sum of the first 10 terms of the geometric sequence. 
math
in an arithmetic sequence whose first term is 4, the 1st, 3rd and 7th terms form consecutive terms of geometric sequence, find the sum of the first three terms of the arithmetic sequence 
arithmetic
in an arithmetic progression the 13th term is 27 and the 7th term is three times the second term find;the common difference,the first term and the sum of the first ten terms