in tan AP if the first term is 22,the common difference is -4 and the sum to n terms is 64 find n.

Asked by riyaliz | 22nd Jul, 2008, 10:08: PM

Expert Answer:

the firstterm = 22 , the common difference = -4

 thesum of   n  terms =  Sn = n/ 2 {  2a +  (n-1) d }  = 64

                                               =  n / 2 { 2 x 22  +  ( n - 1 ) x -4} = 64

                                                  n { 44   -4n + 4 }  = 2 x 64 = 128

                                               = 48 n  - 4 n^2  - 128 = 0

                                                4n^2  - 48 n + 128 =0

                                               4 { n^2 - 12n + 32 } = 0

                                               4 ( n -8 ) ( n-4) =0

                                                     n = 8 , 4

 the number of terms  == 4  , 8

 therefore the A.P. is  22,  18 , 14, 10 , 6, 2 , -2 , -6

                                    the  sum of 4 terms = 64    &      the sum of 8 terms  is also = 64

 

            

Answered by  | 24th Jul, 2008, 07:26: AM

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