Question

If 12th term of the ap is 213 and sum of its first four term is 24. what is sum of first ten terms?

Answer 1

Hi !

Given,

a₁₂ = -13

a + 11d = -13       ---------------------------> (1)

Also,

S₄ = 24
Sn = n/2*(2a + (n-1)d)
     = 4/2 ( 2a + 3d)
     =  2(2a + 3d) = 24

2a + 3d = 12                  -----------------------> (2)

Multiplying eqn(1) with 2

2*[a + 11d =  -13 ] =   2a + 22d = -26       -------------> (3)

solving eqns (2) and (3) , we get :-

2a + 22d = -26
2a + 3d = 12
-------------------
19d = -38

d = -2

Putting this value of "d" , in equation (1) :-

a + 11d  = -13

a - 22 = -13

a = -13 + 22

a = 9

First term = a = 9

Common difference = d = -2

S₁₀ = 10/2 ( 2*9 + 9*-2)
      = 5*(18 - 18)
     = 0

sum of first ten terms of the A.P is zero.

Answer 2

Hello....

Question :- If 12th term of the ap is 213 and sum of its first four term is 24. what is sum of first ten terms?

Answer :- your required answer is in this attachment.