AP calculus
posted by Watermelon .
The sixth term of an Arithmetic Progression is 23 and the sum of the six terms is 78. Find the first term and the common difference.

a+5d = 23
6/2 * [a + (a+5d)] = 78
a + 5d = 23
6a + 15d = 78
a=3
d=4
sequence: 3 7 11 15 19 23
sum: 78 
Given an arithmetic progression 7,3,1,..., state three consecutive terms in this progression which sum up to 75.

The kth term is a+(k1)d
so you want
3a + (k1 + k + k+1)d = 75
3(7) + 3k(4) = 75
12k = 96
k=8
So, the 8th,9th,10th terms are
21,25,29 add up to 75 
I can already tell that's gonna be super hlepufl.