Question

In an ap if s5 plus s7 is equal to 1 6 7 and 8 cm is equal to 235 then find the ap vs and the denotes the sum of the first and terms

Answer 1

We know that sum of n terms sn = n/2(2a + (n - 1) * d)

Given s5 + s7 = 167.

          = 5/2(2a + (5 - 1) * d) + 7/2(2a + (7 - 1)  d) = 167

         = 5/2(2a + 4d) + 7/2(2a + 6d) = 167

         = 5(a + 2d) + 7(a + 3d) = 167

         = 5a + 10d + 7a + 21d = 167

         = 12a + 31d = 167    ---------- (1)


Given that s10 = 235

                  10/2(2a + (10 - 1) * d) = 235

                   5(2a + 9d) = 235

                   2a + 9d = 47     ------------------- (2)


On solving (1) & (2) * 6 , we get

12a + 54d = 282

12a + 31d = 167
----------------------

          23d = 115

         d = 115/23

         d = 5.

Substitute d = 5 in (1), we get

12a + 31d = 167

12a + 31(5) = 167

12a + 155 = 167

12a = 167 - 155

12a = 12

a = 12/12

a = 1.

Therefore the AP is a, a + d, a + 2d  = 1 , 1 + 5, 1 + 5(2), 1 + 5(3).......

Therefore the sum of first n terms = 1,6,11,16.......


Hope this helps!