The 6th term of an arithmetic sequence is x while the 11th term is y. Find the first two terms

I know that it starts by x= a +5d and y= a + 10d
how I don't know where to go from there. Thanks

You're almost there. Subtract x from y and you get y - x = 5d, so therefore d = (y-x)/5. Now subtact 5d from x to find a - you now have values for both "a" and "d" in terms of "x" and "y."

In an arithemetic series, t1 =6 and S9=108. Find the common difference and sum of the first 20 terms.

Do you know the formulae to use?





or



Plug in what you know. One of these will give you an equation which you'll need to solve.

Then use the second formula to find the sum of the first 20 terms, by taking n = 20.

The nth term of an AP is a and the q term is b. Prove the sum of the first (p+q) term is p+q/2(a+b+a-b/p-q)