Question

if 12th term of an ap is 213 and the sum of its 4 term is 24 then what is the sum of its first 10 terms

Answer 1

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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.

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Answer 2

Hello dear your answer








Thanks!!!