1. The difference in the terms values divided by the difference in the number of terms gets d.
Use elimination to get rid of a1 and solve for d.
After you find d you can plug it back into one of the equations and find a1 (the first term)

2. Example:

3. If the sequence is all numerical you will need to know how to do it algebraically.
Sn = (n/2)[a1 + an] use when you know first and last term.
Why does this work?
Find the sum of the first n terms of the sequence {4n + 2}
an = 4n + 2
Sn = 2n2 + 4n

4. Find the sum 2 + 4 + 6 + …+ 2n an = 2n
Find the sum: … First find how many terms (n) make up the sequence. Use an = a1 + (n – 1)d
Since you know the first term, the last term you can find the number of terms (n)
Now use the sum formula to find the total.

5. Examples: