if the sum of certain number of terms of the AP 27,24,21,18,…., is -30 . Find the last term.

Answer

-30

Explanation

Here,`a=27md=(24-27) = -3 and S_(n) = -30` Then,
` n/2.[2a +(n-1)d] = -30 Rightarrow n/2. [54+(n-1)xx(-3)]=-30`
`3n^(2)-57n-60=0Rightarrow n^(2)-19n -20 =0 Rightarrow n=20`
Now, ` S-9n)=-30 Rightarrow n/2 (a+l) -30 Rightarrow 20/2 (27+l) =-30 Rightarrow l= -30`