Question

if the sum of 4th and 8th term is 24 and the sum of 6th and 10th term is 44 find the AP

Answer 1

Let a be the first term and d be the common difference.

Given that the sum of 4th term and 8th term = 24.

a + 3d + a + 7d = 24

2a + 10d = 24

a + 5d = 12   --------------- (1)


Given that the sum of 6th term and the 10th term is 44.

a + 5d + a + 9d = 44

2a + 14d = 44

a + 7d = 22    ----------- (2)


On solving (1) & (2), we get

a + 7d = 22

a + 5d = 12

------------------

       2d = 10

          d = 5.



Substitute d = 5 in (1), we get

a + 5d = 12

a + 5(5) = 12

a + 25 = 12

a = 12 - 25

a = -13.



Therefore the required AP = -13,-8,-3....


Hope this helps!

Answer 2

Let x be the first term and d be a common difference.




------------------   the sum of 4th term and 8th term = 24.

x + 3d + x + 7d = 24

2x + 10d = 24

x + 5d = 12                                                             --------------- (1)





*******************the sum of 6th term and the 10th term is 44.*************

x + 5d + x + 9d = 44

2x + 14d = 44

x + 7d = 22                                            ----------- (2)



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                                         from  (1) & (2)
  , we get

                    x + 7d = 22

                    x + 5d = 12

**********************  

                      = 2d = 10

                                                       =  d = 5.




x + 5d = 12

x + 5(5) = 12

x + 25 = 12

x = 12 - 25

x =  ( -13 ) .



Therefore the required AP =  ************* -13,-8,-3....  *****************