Question

If the sum of first 7 terms of an ap is 119 and sum of first 17 terms is 629. find Sn

Answer 1

Solution:-
Given : S₇ = 119 and S₁₇ = 629
To find : Sn 
Sn = n/2{2a + (n - 1)d}
S₇ = 7/2{2a + (7 -1)d}
119 = 7/2(2a + 6d)
17 = (a + 3d)
a + 3d = 17 .............(1)

S₁₇ = 17/2{2a + (17 - 1)d}
629 = 17/2(2a + 16d)
37 = (a + 8d)
a + 8d = 37 .............(2)

Now, subtracting (1) from (2), we get.

  a + 8d = 37
  a + 3d = 17
 -   -        -
___________
      5d = 20
___________
5d = 20
d = 4
Substituting the value d = 4 in equation (2), we get.
a + 8d = 37
a + 8*4 = 37
a = 37 - 32
a = 5
Now, Sn = n/2{2a + (n -1)d}
= n/2{2*5 + (n - 1)4}
n/2(10 + 4n - 4)
n/2(4n + 6)
n(2n + 3)
2n² + 3n
Answer