Answer :

shivam2000
Yes in an A.P Sn can be negative if the common difference is negative and the first term is not so big. It depends on the values of the A.P. Lets take an example.
a = 5 , n = 10 and d = -2

now , 
[tex]S_n = \frac{n}{2} [ 2a + (n-1)d][/tex]

[tex]S_n = \frac{10}{2} [2*5 + (10 -1)(-2)][/tex] 

Sn = 5(10 - 18)

Sn = -40
yes,it can be if the AP contains both negative oand positive terms.It can happen if common difference is -ve or first term is -ve or both.
Eg.-
-3,-4,-5,-6,-7... be an AP
here,
S5=5/2*{2*(-3)+4*(-1)}
    =5/2*{-6-4}
    =5/2*(-10)
    =-25

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