CBSE Class 10 Answered
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