how many terms of the AP -6,-11 by 2,-5......are needed to give the sum -25.explain the

Asked by riyaliz | 22nd Jul, 2008, 10:55: PM

Expert Answer:

first we have to find the last term :::  Tn =  a + ( n - 1) d ==>   -6  + ( n -1)  ( 0.5) ==> -6 + o.5 (n-1)

  the sum of   n terms = -- 25  == n  /2  {  a  +  l  } ==> n / 2  { -6  +  [ -6 +0.5( n-1)  ] }

                                                                                     ===>  n / 2  { -6  + {  -6  + 0.5 n - 0.5 }]

                                                                                      ===> n / 2 {  -6   -6  +0.5n  -  0.5  }  ==> n / 2 {  -- 12.5  + 0.5 n }

                                         therefore  n / 2 {  - 12.5  + 0.5 n }  = - 25

                                                           --12.5 n   + 0.5 n^2  =  --50 ==> 0.5 n^2  - 12.5 n  + 50 ==0

                                         dividing through out by 0.5   ,,,==>  n ^2  -- 25 n  + 100 ==0

                                                                                                      ( n - 20 ) ( n - 5)  ==0 ==>  n  =20 , 5

                               20  terms  or  5  terms   are     required to get the sum  -- 25  

Answered by  | 23rd Jul, 2008, 12:53: PM

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