the sum of first 50 terms of an AP is 200 and the sum of next 50 terms is 2700.find the AP

Asked by riyaliz | 22nd Jul, 2008, 10:32: PM

Expert Answer:

S50  == 50 / 2 [  2a  +  {50 -1} d ]   == 200

             25  [ 2a  + 49 d ]  = 200

               [ 2a + 49 d ]  = 200  / 25  == 8 ----------(1)

 S 100  -  S 50  =  100 / 2 [  2a  +  ( 100 - 1 ) d ]    --- 50 / 2 [ 2a + ( 50 - 1) d ]  == 2700

                              == 50 [ 2a +99d ]    -- 25 [ 2a +49 d ]  ==2700

                             =  2 [ 2a + 99d  ]  - [ 2a  + 49 d ]   == 2700  / 25  =  108

                             = 4a   +  198 d  --2a --49 d ==108

                            == 2a + 149  d = 108  ---------------(2)

             solving (1)  & (2)

                          2a +49 d = 8

                          2a + 149 d = 108

                                100 d  =  100  =====> d = 1

  substituting this value  in the  equation (1)

                                    2a + 49 (1)   == 8

                                     2a == 8  - 49  == --41

                                       a  == -- 20  ..5

 so the A.P is --20.5 ,, --19.5,,--18.5 ...................... 100 terms

                              

 

 

Answered by  | 23rd Jul, 2008, 05:02: PM

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