CBSE Class 10 Answered
Dear Student,
AP : 20, 58 / 3 , 56 / 3..............
First term (a) = 20
Common Difference (d) = (58 / 3) - 20 = (-2 / 3)
Sum of n term (S n) = 300
Apply : Sum of n term (S n) = [n/2] x(2a + (n-1)xd )
300 = [n/2] x ( 2x{20} + (n-1)x{-2 / 3} )
300 * 2 = n ( 40 + [- 2 / 3] n - [-2 / 3] )
600 = n ( 40 x 3 - 2 n +2) / 3
1800 = n ( 120 + 2 - 2n )
1800 = n ( 122 - 2n)
Divide the whole equation by "2"
900 = n ( 61 - n )
n2 - 61n + 900 = 0
n2 +(- 61n) + 900 = 0
Apply Splitting the middle term : 900 = -36 x -25
n2 +(-36n - 25n) + 900 = 0
n ( n - 36) -25 (n - 36) = 0
So : (n-36) x ( n - 25) = 0
=> ( n -36 ) = 0 OR ( n - 25) = 0
=>The total Number of term is (n) = 36 or 25
The AP IS IN A DESCENDING ORDER SO THE DOUBLE ANS CAN BE EXPLAINED IN TERMS OF THE SUM OF N TERMS.
SINCE THE AP IS IN A DESCENDING THERE IS A POSSIBILITY FOR NEGETIVE NUMBERS TO OCCUR IN THE AP SO THAT IS WHY THE SUM OF N TERM WHICH IS 300 CAN BE OF FOR FIRST 26 TERMS OR FOR FIRST 35 TERMS OF AP .
That is why there is a occourence of double.
Thanks and Regards
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