SOLUTION: if the 3rd term of an arithmetic sequence is 13 and the 9th term is 37, what is the common difference

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Question 1166963: if the 3rd term of an arithmetic sequence is 13 and the 9th term is 37,
what is the common difference
Answer by Edwin McCravy(20063) About Me  (Show Source):
You can put this solution on YOUR website!
Instead of doing the problem for you, I'll do one exactly like yours,
step by step:

if the 4th term of an arithmetic sequence is 21 and the 11th term is 56,
what is the common difference?

__, __, __, 21, __, __, __, __, __, __, 56,...

a%5Bn%5D=a%5B1%5D%2B%28n-1%29d

when n=4, a4=21

a%5B4%5D=a%5B1%5D%2B%284-1%29d
21=a%5B1%5D%2B3d

when n=11, a11=56

a%5B11%5D=a%5B1%5D%2B%2811-1%29d
56=a%5B1%5D%2B10d

So we have this system

system%28a%5B1%5D%2B3d=21%2Ca%5B1%5D%2B10d=56%29

Solve the first equation for a1

a%5B1%5D=21-3d

Substitute (21-3d) for a1 in

a%5B1%5D%2B10d=56
%2821-3d%29%2B10d=56
21-3d%2B10d=56
21%2B7d=56
7d=35
d=5

The common difference is 5.

Now do yours the exact same way.

It's not necessary, but if you like you can find the 
first term by substituting d=5 in

a%5B1%5D=21-3d
a%5B1%5D=21-3%285%29
a%5B1%5D=21-15
a%5B1%5D=6

and find the arithmetic sequence to be:

6, 11, 16, 21, 26, 31, 36, 41, 46, 51, 56,...
 
Edwin