If this is an arithmetic sequence, then *d* = 2 because that's the size of the step from *a*_{5} to *a*_{6}. We must have taken 4 steps to get from *a*_{1} to *a*_{5}. Working backwards by stepping down 2 each time, we can fill in *a*_{4}, *a*_{3}, *a*_{2}, and finally *a*_{1}. We find that *a*_{1} = 3. Here's another way to do the example. Whatever *a*_{1} is, we took 4 steps of size 2 to get to *a*_{5}. In symbols, *a*_{1} + 4(2) = *a*_{5}.
Since we know *a*_{5} = 11, we can solve this equation for *a*_{1}. *a*_{1} + 4(2) = 11
*a*_{1} = 3
Thankfully, we got the same answer as before. | |