Question

In an AP if the 12th term is-13 and the sum of its first four term is 24.find the sum of its first 20 terms

Answer 1

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Answer 2

Answer:

Sum of the first 20 terms = -200

Step-by-step explanation:

12th term of AP

a + 11d = -13   ---1)

Sum of first four terms

(a) + (a+d) + (a+2d) + (a+3d) = 24

4a + 6d = 24    ---2)

Adding 1) and 2)

 a + 11d = -13   ---1)          (Multiply 1) by 4 and multiply 2) by 1

4a + 6d = 24   ---2)

4a + 44d = -52

4a +  6d  = 24

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-        -          -

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           38d = -76

               d = -76/38

               d = -2

Substitute d = -2  in eq 1)

a + 11d = -13

a + 11x-2 = -13

a -22   = -13

     a    = -13 +22

     a = 9

Therefore a=9 and d= -2

Using Sum of n terms formula we get

$S_{20} = n/2 (2a + (n-1)d)$

      =20/2 (2x9 +(20-1)-2)

       =10 ( 18 + 19 * -2)

       = 10 (18 -38)

       = 10 * -20

       = -200

Therefore sum of 20 terms of the AP is -200

Hope this helps!!!