Thread: Arithmetic Sequence Sums to be PROVEN

I have a problem which I have the answer to but I don't understand why and how to prove it?

If the sum of the first 10 terms of an a.p. is 120, sum of the first 20 =840. find sum of first 30 terms....

I believe the answer to be 2160 but I don't understand why...

SUM = n[2a + d(n - 1)] / 2 ; n = number of terms, a = 1st term, d = common difference

10[2a + d(10 - 1)] / 2 = 120 ; simplify: 2a + 9d = 24 [eq. 1]

20[2a + d(20 - 1)] / 2 = 840 ; simplify: 2a + 19d = 84 [eq. 2]

Get a and d using 2 above equations. Then apply to n = 30. OK?

Ah ha
Thank You.
I think I get it now!