Advertisement Remove all ads

In an A.P., if S5 + S7 = 167 and S10=235, then find the A.P., where Sn denotes the sum of its first n terms. - Mathematics

Sum

In an A.P., if S5 + S7 = 167 and S10=235, then find the A.P., where Sn denotes the sum of its first n terms.

Advertisement Remove all ads

Solution

`"S"_5+ "S"_7= 167 and "S"_10=235`

Now `"S"_n=n/2[ 2a + (n-1) d  ]`

`"S"_5 + "S"_7=167`

⇒ `5/2 [ 2a + 4d ] + 7/2 [ 2a + 6d ] =167`

⇒  12a + 31d = 167                     .......(i)

also `"S"_10=235`

∴  `10/2 [ 2a + 9d ] = 235`

2a + 9d = 47                          .........(ii)

Multiplying equation (2) by 6, we get

   12a + 54d = 282                    .....(3)

(-) 12a + 31d = 167
     -      -           -     
              23 d = 115

`therefore d = 5`

Substituting value of d in (2), we have
2a + 9(5) = 47
2a + 45 = 47
2a = 2
a = 1
Thus, the given A.P. is 1, 6, 11, 16 ,..........

  Is there an error in this question or solution?
Advertisement Remove all ads
Advertisement Remove all ads
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×