progreIn a certain Ap the sum of the first and fifth term is 6 more than the 3rd term.Show that the sum of the first 10 terms of thession is 160.
a + a+4d = 6 + a+2d
2(a+2d) = 6 + (a+2d)
a + 2d = 6
There are lots of APs that will work:
0,3,6,9,12
2,4,6,8,10
4,5,6,7,8
So now if you want the sum to be 160, you need
5(2a+9d) = 160
Solve these two equations for a and d.