Question 909311
The first term of an arithmetical progression is 11 and the sums of the first five and the first ten terms respectively are equal in magnitude but different in sign.Find the second term of the progression.

a=11

S5 =-S10
sum of n terms


Sn = n/2(2a+(n-1)d)
S5 =5/2(2*11+(5-1)d)
=5/2(22+4d)
=5(11+2d)


S10= 10/2(22+(9*d))

=5(22+9d)

5(11+2d)=-5(22+9d)
55+10d=-110-45d
-55d=165
d=-3

S2= 2/2(2*11-3)

=19


S2=19